Thermodynamics-I

Lecture No.03Akbar Ali Qureshi

Lecturer Email: akbaraliqureshi@bzu.edu.pk

Contact no: 0335-6387138 Mechanical Engineering Department

UCE&T, BZU Multan.

Thermal EquilibriumTwo bodies are said to be at thermal equilibrium if they are at the same temperature. This means there is no net exchange of thermal energy between the two bodies. The top pair of objects are in contact, but since they are at different temps, they are not in thermal equilibrium, and energy is flowing from the hot side to the cold side.

hot coldheat

26 °C 26 °C

No net heat flow

The two purple objects are at the same temp and, therefore are in thermal equilibrium. There is no net flow of heat energy here.

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Temperature and Zeroth Law of Thermodynamics

• The zeroth law of thermodynamics: If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other.

• By replacing the third body with a thermometer, the zeroth law can be restated as two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact.

Two bodies reaching thermal equilibrium after being brought

into contact in an isolated enclosure.

The Zeroth Law of ThermodynamicsWe have already discussed the zeroth law, and include it here for completeness:If object A is in thermal equilibrium with object C, and object B is separately in thermal equilibrium with object C, then objects A and B will be in thermal equilibrium if they are placed in thermal contact.

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Temperature Scales• All temperature scales are based on some

easily reproducible states such as the freezing and boiling points of water: the ice point and the steam point.

• Ice point: A mixture of ice and water that is in equilibrium at 1 atm pressure (0°C or 32°F).

• Steam point: A mixture of liquid water and water vapor (with no air) in equilibrium at 1 atm pressure (100°C or 212°F).

• Celsius scale: in SI unit system• Fahrenheit scale: in English unit system

• Thermodynamic temperature scale: A temperature scale that is independent of the properties of any substance.

• Kelvin scale (SI) Rankine scale (E)• A temperature scale nearly identical to the

Kelvin scale is the ideal-gas temperature scale.

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Pressure

The normal stress (or “pressure”) on the feet of a chubby person is much

greater than on the feet of a slim person.

Pressure: A normal force exerted by a fluid per unit area

68 kg 136 kg

Afeet=300cm2

0.23 kgf/cm2 0.46 kgf/cm2

P=68/300=0.23 kgf/cm2

Equation of state In thermodynamics, an equation of state is a

relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions. It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy.

Boyle’s law & Charles law Boyle's law Boyle noted that the gas volume varied inversely with the

pressure. In mathematical form, this can be stated as:

Charles's law In 1787 Jacques Charles indicated a linear relationship between

volume and temperature:

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions. The ideal gas law is often introduced in its common form:

where P is the absolute pressure of the gas, V is the volume of the gas, n is the amount of substance of gas (measured in moles), T is the absolute temperature of the gas and R is the ideal, or universal, gas constant.

In SI units, P is measured in Pascal, V is measured in cubic meters, n is measured in moles, and T in Kelvin (273.15 Kelvin = 0 degrees Celsius). R has the value 8.314 J·K−1·mol−1 or 0.08206 L·atm·mol−1·K−1 if using pressure in standard atmospheres (atm) instead of Pascal, and volume in liters instead of cubic meters.

Ideal gas law

Molar form

By replacing n with m / M, and subsequently introducing density

ρ = m/V, we get:

Ideal Gas Equation

WorkWork is a Mechanical form of Energy:

DistanceForceWork

xFdW

pdVdW ∆X

Force

e.g. Raising Piston,

WorkWork is the energy

transferred between a system and environment when a net force acts on the system over a distance.

Work is positive when the force is in the direction of motion.

Work is negative when the force is opposite to the

motion.

Heat• The energy transferred in a thermal interaction is called heat.• The symbol for heat is Q.• The energy equation now becomes ΔEsys = ΔEmech + ΔEth = Wext + Q

Quick quiz: A gas cylinder and piston are covered with heavy insulation. The piston is pushed into the cylinder, compressing the gas. In the process. The gas temperature

• Increases• Decreases• Doesn’t change

Heat and Thermal interactions

Distinguish between Heat, Temperature, and Thermal energy

Thermal energy is an energy of the system due to the motion of its atoms and molecules. Thermal energy is a state variable, it may change during a process. The system’s thermal energy continues to exist even if the system is isolated and not interacting thermally with its environment

Heat is energy transferred between the system and the environment as they interact. Heat is not a particular form of energy, nor is it a state variable. Heat may cause the system’s thermal energy to change, but that does not mean that heat and thermal energy are the same thing.

Temperature is a state variable, it is related to the thermal energy per molecule. But not the same thing.

Internal EnergyInternal energy (also called thermal energy) is the energy an object or substance is due to the kinetic and potential energies associated with the random motions of all the particles that make it up. The kinetic energy is, of course, due to the motion of the particles. To understand the potential energy, imagine a solid in which all of its molecules are bound to its neighbors by springs. As the molecules vibrate, the springs are compressed and stretched.

The hotter something is, the faster its molecules are moving or vibrating, and the higher its temperature. Temperature is proportional to the average kinetic energy of the atoms or molecules that make up a substance.

Internal Energy

Internal Energy vs. HeatThe term heat refers is the energy that is transferred from one body or location due to a difference in temperature. This is similar to the idea of work, which is the energy that is transferred from one body to another due to forces that act between them. Heat is internal energy when it is transferred between bodies.

Technically, a hot potato does not possess heat; rather it possesses a good deal of internal energy on account of the motion of its molecules. If that potato is dropped in a bowl of cold water, we can talk about heat: There is a heat flow (energy transfer) from the hot potato to the cold water; the potato’s internal energy is decreased, while the water’s is increased by the same amount.

Temperature vs. Internal Energy

Temperature and internal energy are related but not the same thing. Temperature is directly proportional to the average molecular kinetic energy.

Consider a bucket of hot water and a swimming pool full of cold water. The hot water is at a higher temperature, but the pool water actually has more internal energy! This is because, even though the average kinetic energy of the water molecules in the bucket is much greater than that of the pool, there are thousands of times more molecules in the pool, so their total energy is greater.

First Law of Thermodynamics

Energy is always conserved. It can change forms: kinetic, potential, internal etc., but the total energy is a constant. Another way to say it is that the change in thermal energy of a system is equal to the sum of the work done on it and the amount of heat energy transferred to it.

First Law of Thermodynamics

PdV WorkLet the Piston be moving from Thermodynamic Equilibrium State 1 (P1, V1) to State 2 (P2, V2).Let the values at any intermediate Equilibrium State is given by P and V. State 2State 1

P1 V1

P2 V2

Area A

For an Infinitesimal displacement, dL, the Infinitesimal Work done is;

Similarly, for Process 1 – 2; we can say that;

2

1

21

V

V

PdVW

VolumePr

essu

re Quasi-Static Process Path

P1

P2

V1 V2

dW = F * dL = P*A*dL = PdV

PdV Work

)( 1221

2

1

VVPPdVWV

V

Pres

sure

(P)

Volume (V)

P=ConstIsobaric

W1-2

State 1 State 2

V2V1

• An isobaric process is a constant pressure process. ΔU, W, and Q are generally non-zero, but calculating the work done by an ideal gas is straightforward

W = P·ΔV• Water boiling in a saucepan is an example of an isobar process

• Isobaric Process

Pres

sure

(P) V=Const

Isochoric

Volume (V)

State 1

State 2P2

P1

02

1

21

V

V

PdVW

PdV Work

• An isochoric process is a constant volume process. When the volume of a system doesn’t change, it will do no work on its surroundings. W = 0

ΔU = Q• Heating gas in a closed container is an isochoric process

• Isochoric Process

2

111

1

2111121

1111

21

lnln2

1

2

1

PPVP

VVVP

VdVVPW

VVPPCVPPV

PdVW

V

V

V

V

PdV WorkIsothermal Process:

Pres

sure PV = C

Quasi-Static

Volume

State 1

State 2P2

P1

V1 V2

An isothermal process is a constant temperature process. Any heat flow into or out of the system must be slow enough to maintain thermal equilibrium

For ideal gases, if ΔT is zero, ΔU = 0 Therefore, Q = W. Any energy entering the system (Q) must leave as work

(W)

nn

nnnnnn

n

V

V

nn

V

Vn

n

V

V

n

nnnn

PP

nVP

nVPVP

nVXVPVXVPVV

nVP

nVVP

VdVVPW

PdVW

VVPPCVPVPPV

/1

1

2112211

1111

12221

11

211

1

111121

21

112211

111

11

1

2

1

2

1

2

1

PdV WorkPr

essu

re

PVn = C

Volume

1

2P2

P1

n =1

n =3 n =2

n =∞

An adiabatic process transfers no heattherefore Q = 0

ΔU = Q – W When a system expands adiabatically, W is positive (the system does work) so ΔU is negative. When a system compresses adiabatically, W is negative (work is done on the system) so ΔU is

positive.

The End