AP PHYSICS

Thermodynamics I

RECAP

Thermal PhysicsEquations not on the equation sheet

c specific heat units J(kgK)

L Latent Heat units Jkg

TmcQ

mLQ

The Mole

Quantity in Physics mass ndash quantitative measure of objectrsquos inertia

mole ndash number of particles

Mole amp Mass

Every substance has a unique relationship between its mass and number of moles

Molar Mass (M)the ratio of the mass of a substance in grams to the number of

moles of the substance

How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the

substance in units of grams rather than atomic mass units

Ex What is the molar mass of O2

Methane

What is the molar mass (M) of CH4

What number of moles (n) are there in 40 g of methane gas

How many molecules (N) of CH4 does this include

What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)

Note n number of moles N number of particles

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

RECAP

Thermal PhysicsEquations not on the equation sheet

c specific heat units J(kgK)

L Latent Heat units Jkg

TmcQ

mLQ

The Mole

Quantity in Physics mass ndash quantitative measure of objectrsquos inertia

mole ndash number of particles

Mole amp Mass

Every substance has a unique relationship between its mass and number of moles

Molar Mass (M)the ratio of the mass of a substance in grams to the number of

moles of the substance

How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the

substance in units of grams rather than atomic mass units

Ex What is the molar mass of O2

Methane

What is the molar mass (M) of CH4

What number of moles (n) are there in 40 g of methane gas

How many molecules (N) of CH4 does this include

What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)

Note n number of moles N number of particles

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

The Mole

Quantity in Physics mass ndash quantitative measure of objectrsquos inertia

mole ndash number of particles

Mole amp Mass

Every substance has a unique relationship between its mass and number of moles

Molar Mass (M)the ratio of the mass of a substance in grams to the number of

moles of the substance

How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the

substance in units of grams rather than atomic mass units

Ex What is the molar mass of O2

Methane

What is the molar mass (M) of CH4

What number of moles (n) are there in 40 g of methane gas

How many molecules (N) of CH4 does this include

What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)

Note n number of moles N number of particles

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Mole amp Mass

Every substance has a unique relationship between its mass and number of moles

Molar Mass (M)the ratio of the mass of a substance in grams to the number of

moles of the substance

How do you determine Molar Massthe mass of 1 mole of a substance equals the atomic mass of the

substance in units of grams rather than atomic mass units

Ex What is the molar mass of O2

Methane

What is the molar mass (M) of CH4

What number of moles (n) are there in 40 g of methane gas

How many molecules (N) of CH4 does this include

What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)

Note n number of moles N number of particles

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Methane

What is the molar mass (M) of CH4

What number of moles (n) are there in 40 g of methane gas

How many molecules (N) of CH4 does this include

What is the mass of 2408 x 1023 molecules of ethanol (C2H5OH)

Note n number of moles N number of particles

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Ideal Gases Volume and Number

The behaviors of ideal gases at low pressures are relatively easy to describe

The volume V is proportional to the number of moles n and thus to the number of molecules (this concept stems from Avogadrorsquos Law)

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Ideal Gases Boylersquos Law

Robert Boyle (1627 ndash 1691) Irish physicist and chemist who employed Robert Hooke as

an assistant (you know the Hookersquos law guy and the ldquocellrdquo guy)

Boylersquos LawThe volume V varies inversely with the pressure P

when temperature (T) and amount of gas (n) are constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Ideal Gases Charlesrsquo Law

Jacques Charles (1746 ndash 1823) French inventor physicist and hot air balloonist

Charlesrsquo LawThe pressure P is directly proportional to the

absolute temperature T (temperature in Kelvin) when volume V and amount n are constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Ideal Gas Law

Combining of Boylersquos Law and Charlesrsquo Law

Adding Avogadrorsquos Law yields

R is the ideal gas constant or R = 008206

L∙atm(mol∙K)

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Gas at STP

The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC and a pressure of 1 atm (1013 x 105 Pa) If you want to keep 1 mole of an ideal gas in your room at STP how big is the Tupperware that you need

[Answer in units of liters 1 m3 = 1000 L]

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Kinetic Theory of an Ideal Gas

Assumptions of the Kinetic-Molecular Model1 A container with volume V contains a very large number N of

identical molecules each with mass m The container has perfectly rigid walls that do not move

2 The molecules behave as point particles their size is small in comparison to the average distance between particles and to the dimensions of the container

3 The molecules are in constant random motion they obey Newtonrsquos laws Each molecule occasionally makes a perfectly elastic collision with a wall of the container

4 During collisions the molecules exert forces on the walls of the container these forces create the pressure that the gas exerts

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Kinetic Theory of an Ideal Gas

For an ideal gas the average kinetic energy Kavg per molecule is proportional to the absolute (Kelvin) temperature T

The ratio RNo occurs frequently in molecular theory and is known as the Boltzmann constant kB

What is the value of the Boltzmann constant including units

Ludwig Boltzmann (1844 ndash 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Molecular Speeds in an Ideal Gas

If molecules have an average kinetic energy Kavg given by the equation

then what is their average speed

TkK Bavg 23

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Five Molecules

Five ideal-gas molecules chosen at random are found to have speeds of 500 600 700 800 and 900 ms respectively Find the rms speed for this collection Is it the same as the average speed of these molecules

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

The Boltzmann Constant Gets Around

Starting with the typical ideal gas law (PV = nRT ) derive an expression for the gas law that includes both the Boltzmann Constant kB and the number of molecules of an ideal gas N

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Kinetic Energy of A Molecule

a) What is the average (translational) kinetic energy of a molecule of oxygen (O2) at a temperature of 27oC assuming that oxygen can be treated as an ideal gas

b) What is the total (translational) kinetic energy of the molecules in 1 mole of oxygen at this temperature

c) Compare the root-mean-square speeds of oxygen and nitrogen molecules at this temperature (assuming that they can be treated as ideal gases)

[mass of oxygen molecule mO2 = 531 x 10-26 kg mass of nitrogen molecule mN2 = 465 x 10-26 kg]

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Internal Energy

DWT

Particles in a system (like an ideal gas) are in motion Therefore

1 the particles have some velocity

2 the particles have some kinetic energy3 the system as a whole has some internal energy as a result of

the individual particlesrsquo kinetic energy

This is true of material in any phase (solid liguid gas plasma)

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Internal Energy amp Temperature

Kinetic Energy of the individual particles

The system as a whole has some internal energy as a result of the individual particlesrsquo kinetic energy

Kinetic energy of all the particles

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

First Law of Thermodynamics

DWT

Thermodynamics is the study of energy relationships that involve heat mechanical work and other aspects of energy and energy transfer

There are two ways to transfer energy to an object1 Heat the object2 do Work on the object

Both of these energy transfer methods add to the internal energy of the object

The First Law of Thermodynamics (1LT)

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Work Done during Volume Change

Classic Thermodynamic SystemGas in a cylinder confined by a piston

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

PV Diagrams

Area under the curve is the work done by the

gas

Notice the arrow denoting direction of the

process

Work

Pressure

VolumeVo Vf

P

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Thermodynamic Processes

Four Processes1Isothermal2Isobaric3Isochoric (Isovolumetric)4Adiabatic

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Isothermal

The curve represents pressure as a function of volume for an ideal gas at a single temperature The curve is called an isotherm

For the curve PV is constant and is directly proportional to T (Boylersquos Law)

Volume

Pressure

Va Vb

Pa

Pb

Work

For Ideal Gases

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Isobaric

The curve is called an isobar

The pressure of the system (system - constant amount of gas n) changes as a result of heat being transferred either into or out of the system andor work done on or by the system

Volume

Pressure

Va Vb

P

Work

isotherms

Ta

Tb

Ta gt Tb

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Isochoric (Isometric or Isovolumetric)

The curve is called an isochor

There is no work done in this process All of the energy addedsubtracted as heat changes the internal energy

Volume

Pressure

V

Pa

isotherms

Pb

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Adiabatic

The curve is called an adiabat

No heat is transferred into or out of the system (An adiabatic curve at any point is always steeper than the isotherm passing through the same point)

Volume

Pressure

Va Vb

Pa Wor

kisotherms

Pb

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Isobaric Example

Thermodynamics of Boiling WaterOne gram of water (1 cm3) becomes 1671 cm3 of steam

when boiled at a constant pressure of 1 atm (1013 x 105 Pa) The latent heat of vaporization at this pressure is Lv = 2256 x 106 Jkg Compute

a) the work done by the water when it vaporizesb) its increase in internal energy

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Isochoric (Isovolumetric) Example

Heating WaterWater with a mass of 20 kg is held at constant volume in

a container while 10000 J of heat is slowly added by a flame The container is not well insulated and as a result 2000 J of heat leaks out to the surroundings

a)What is the increase in internal energyb)What is the increase in temperature

[the specific heat of water is 4186 Jkg∙oC]

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Molar Heat Capacities

The amount of heat Q needed for a certain temperature change ΔT is proportional to the temperature change and to the number of moles n of the substance being heated

where C is a quantity different for different materials called the molar heat capacity of the material

Units of C J(mol∙K) Relation of specific heat (c) to molar heat capacity (C) is the molar

massC = Mc

Because of 1LT the molar heat capacities are not the same for different thermodynamic processeshellip

Q = nCΔT

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

The molar heat capacities are different for isochoric (constant volume) and isobaric (constant pressure) processes

1LT ΔU = Q+W Q = ΔU ndash W

IsochoricW = -PΔV = 0

Q = ΔU ndash o

Q = ΔU

All of the heat gainedlost results directly in a change in internal energy

Molar heat for a constant volume Cv

IsobaricFor pressure to remain constant the

volume must change

W = -PΔV

Q = ΔU + PΔV

Some of the heat gained by the system is converted into work as the system expands

Molar heat for a constant pressure Cp

Molar Heat Capacities amp 1LT

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant

Relationship between Cv and Cp

Cp = Cv + RR universal gas constant