ThermodynamicsSOME DEFINITIONS:• THERMO – related to heat• DYNAMICS – the study of motion• SYSTEM – an object or set of objects• ENVIRONMENT – the rest of the universe• MICROSCOPIC – at an atomic or molecular level• MACROSCOPIC – at a level detectable by our senses

THERMODYNAMICSis the study of the relationship between heat and motion. is a macroscopic description of the properties of a system using state variables (e.g. volume, temperature, pressure)

Atoms are in constant motion, which increases with temperature.

The Phases of Matter

+ - + - + - - +- + - + - + - + -- - + - + - + + -- - + - + - + + -- - + - + - + + -- - + - + - + + -- - + - + + + -

+ - + - + - + + -- - + - + - + -

- - + - + - + + -+ - + - + - + -

Solid Liquid Gas or Vapor Plasma

Increasing TemperatureSolids and liquids composed of atoms joined together at distances of about 10-10 m by attractive electrical forces. In gases, vaporsand plasmas, the atoms, molecules or ions are in random motion.

TemperatureTemperature• is a measure of how hot or cold an object is.• is measured by a thermometer.

Thermometers are based on physical properties of objects that change with temperature, for example:

volume of a liquidlength of a solidpressure of a gaselectrical resistance of a solidelectrical potential difference between two solids.

Common Temperature ScalesFahrenheit:• Based on the ability of farm animals to survive for

extended periods without attention. (0 F is the coldest and 100 F is the hottest).

Celsius or Centigrade:• Based on the physical properties of water on the

earth’s surface at sea level (0 C is the freezing point and 100 C is the boiling point).

T( C) = (5/9)[T( F) – 32]T ( F) = (9/5)T( C) + 32

Zero’th Law of ThermodynamicsOur experience tells us that objects placed in contact

will eventually reach the same temperature. We say that they are then in thermal equilibrium. This is the basis for

The Zero’th Law of Thermodynamics:If two objects A and B are in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.

Objects or systems in thermal equilibrium have the same temperature. This is the physical basis for the definition of temperature.

Questions• Is it possible for two objects to be in

thermal equilibrium if they are not touching each other?

• Can objects that have different temperatures be in thermal equilibrium with each other?

Thermal ExpansionMost materials expand when heated:

The average distance between atoms increases as the temperature is raised.The increase is proportional to the change in temperature (over a small range).

Consider an object of length Li at temperature TiIf the object is heated or cooled to temperature Tf

Lf – Li = α Li (Tf – Ti) or ∆L = α Li ∆Tα = coefficient of linear expansion [ºC-1]

(α is a property of the material)

Thermal Expansion of Solids and Liquids

For the same temperature change, the thermal expansion of liquids is much greater than that of solids (> 10 times).

Area Expansion:∆A = 2α Ai ∆T

Volume Expansion∆V = 3α Vi ∆T

12 x 10-6Concrete

3.2 x 10-4Gasoline

1.8x 10-4Mercury

29 x 10-6Lead

17 x 10-6Copper

9 x 10-6Glass

α (ºC -1)Material

Example: Thermal Expansion

Problem 17-8. A concrete highway is built of slabs

12 m long (20 ºC). How wide should the expansion cracks between the slabs be (at 20 ºC) to prevent buckling if the range of temperature is –30 ºC to +50 ºC ?

Liquid water has an unusual property.• Water contracts when

heated from 0ºC to 4ºC, then expands when heated from 4 ºC to 100 ºC.

• Just above the freezing point, the coldest (and least dense) water rises to the surface, and lakes freeze from the surface downward.

• This unusual property permits aquatic life on earth to survive winter!

Density of Water

0.95

0.96

0.97

0.98

0.99

1

0 4 12 20 50 100

Temperature in Celsius

g/(c

m**

3)

Thermal Stress

TEAF

TLLAF

E

TLL

LAF

EL

∆=

∆=

∆=∆

=∆

α

α

α

00

0

0

1

1

• Heat can stress materials if no allowance is made for thermal expansion:

E = Young’s Modulus

Thermal Expansion

Thermal Stress

Review Questions• When a cool mercury or alcohol

thermometer is inserted into boiling water, it will initially indicate a lower temperature before the reading starts to increase. Explain.

• Will a grandfather clock that has been calibrated at normal room temperature run fast, slow or the same on a very hot day?

Absolute (Kelvin) Temperature ScaleThe volume occupied by any gas at constant pressure is an

increasing linear function of temperature, that alwaysextrapolates to zero at –273.15 ºC (called absolute zero).

This is called Charles’s Lawand is the basis for the absolute or Kelvin (K)temperature scale.T(K) = T(ºC) + 273.15

Absolute or Kelvin Temperature ScaleThe absolute or Kelvin scale is the true physical temperature scale.

T = -273.15 ºC = 0 K is the lowest temperature that can be defined for any physical system.

Absolute zero of temperature (0 K) is a theoretical limit that can never be reached in a physical system.

Experiments on Bose-Einstein Condensation in gases have reached the nano-Kelvin (10-9 K) range (1998, 2001 Nobel Prizes in physics)!

The degree steps in the Celsius and Kelvin scales are chosen to be the same: ∆T(ºC) = ∆T(K).

Molecular Model of an Ideal Gas• The number of molecules is large.• The average separation between molecules

is large compared to their dimensions.• The molecules obey Newton’s laws of motion

and move randomly.• The molecules collide elastically with each

other and with the container walls.• The forces between molecules are negligible

except during collisions.• All the molecules of the gas are identical.

Ideal GasThe relationship between the state variables, pressure P, volume V and temperature T of a system is called its equation of state.An ideal gas is one whose equation of state is simple:

PV = nRTn = number of moles (mole = 6.023 x 1023 molecules)R = universal gas constant = 8.31 J/(mole K)Most gases near room temperature and atmospheric pressure behave as ideal gases.

Avogradro’s Number and Molar Mass• NA = 6.023 x 1023 = Avogadro’s number

• 1 mole is the quantity of any substance that contains Avogadro’s number of atoms or molecules.

• The gram-molecular-weight M of a substance is the mass of one mole (molar mass) of that substance:

Helium (He) M = 4 g/moleNitrogen (N2) M = 28 g/moleOxygen (O2) M = 32 g/moleMethane (CH4) M = 16 g/mole

Equation of State of an Ideal Gas• For a gas containing N atoms or molecules, the

number of moles n = N/NA.

• The ideal gas law:PV = nRT = (N/NA)RT = N(R/NA)T = NkBTwherekB = R/NA = 1.38 x 10-23 J/K (Boltzmann’s constant)

• The ideal gas law may be expressed:PV = NkBT (N = number of atoms or molecules)

orPV = nRT (n = number of moles)

Applying the Ideal Gas LawFor a ideal gas:

INITIAL STATE (1) FINAL STATE (2)P1, V1, T1, n1 P2, V2, T2, n2

P1V1 = n1RT1 P2V2 = n2RT2

R = P1V1/(n1T1) R = P2V2/(n2T2)

22

22

11

11

TnVP

TnVP =

2

22

1

11

TVP

TVP =or if n1 = n2

general case closed container

Example Problem Problem 17-34.

If 18.75 mol of helium gas is at 10.0ºC and a gauge pressure of 0.350 atm., calculate

a) The volume of the helium gas under these conditions.

b) The temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

Questions• An ideal gas in a sealed bottle at temperature T

occupies a volume V, and exerts a pressure P on the walls of the bottle. What will happen to the pressure if the temperature is doubled?

• Instead of a sealed container, the gas is contained in a test tube with a movable piston on one end. The temperature is then halved. What will happen toa) the pressure?b) the volume?