Physics 213: Unit 2

Temperature, Heat, and the Zeroth Law of Thermodynamics

Thermodynamics

Thermodynamics deals with an internal energy of the systems, the thermal energy, and is governed by the Laws of Thermodynamics

Thermal Temperature

Zeroth Law of Thermodynamics

Temperature in daily life:

HOT WARM COOL COLD

What is the definition of temperature ?How to measure the temperature?

0th Law

0th Law of Thermodynamics

If body A and B are each in thermal equilibrium with a third body T, then they are in thermal equilibrium with each other.

Thermal equilibrium: two objects in thermal contact cease to have any exchange of heat.

Thermal contact : Heat can be exchanged.

Heat: energy exchanged between objects due to their temperature difference.

Temperature : two objects in thermal equilibrium with each other are at the same temperature

Measuring Temperature

Bring a thermometer to a thermal equilibrium with the object

Thermometer: physical property changes with temperature

— pressure of gas at constant volume— length of solid— Electric resistance— Volume of liquid

Temperature Scales

DEFINE: Freezing temperature of water: 0˚C

Boiling temperature of water: 100˚C

Constant-volume gas thermometer: Measure Pressure Temperature

Different gases all extrapolate to zero pressureat -273˚C: Kelvin scale

Celsius scale

Temperature Scales

Kelvin scale: T = 0 K for P = 0 point

Celsius scale: Tc = T - 273.15˚

Fahrenheit scale: TF = 9/5 Tc + 32˚

Thermodynamic scale: triple point of waterT3 = 273.16 K

Thermal Expansion

When heated, objects expand.

Linear expansion: L LT Temperature changes this much

Original length

Length changesthis much

Coefficient of linear expansion

L / L

T

Volume expansion: V VT

Coefficient of volume expansion

V / V

T 3

Unusual Behavior of Water

The maximum density occurs at 4 ˚C:

Above 4 ˚C, expands when heateduntil 100 ˚C;

Below 4 ˚C, expands when cooleduntil 0 ˚C.

Temperature and Heat

Internal energy: the energy of a system when it is stationary - nuclear, chemical, strain, etc.

Thermal energy: the energy that changes when the temperature changes, associated with motions of atoms, molecules, etc.

Heat QHeat Q: the transferred energy.

Units of Heat

Calorie: amount of heat to heat 1 g of water from 14.5 to 15.5 ˚C

BTU: amount of heat to heat 1 lb of water from 63 to 64 ˚F

SI: Joule (the same as energy)

Joule’s experiment: 1 cal = 4.186 J

P

T(K)0

0

Constant-volume gas thermometer: P-T curve extrapolates to origin.

pb

p3

Tb(K )

T3(K )

373.15

273.16

HRW 2E (5th ed.). Suppose the temperature of a gas at the boiling point of water is 373.15 K. What then is the limiting value of the ratio of the pressure of the gas at that boiling point to its pressure at the triple point of water? (Assume the volume of the gas is the same at both temperatures.)

(a) TF = (9/5)TC + 32˚For TF = (9/5)TF + 32˚we get TF = -40 ˚F

(b) TF = (9/5)TC + 32˚ = (9/5)(T - 273.15) + 32˚

For TF = (9/5) (TF - 273.15) + 32˚we get TF = 575 ˚F

(c) Since

TC = T - 273.15

the Kelvin and Celsius temperatures can never have thesame numerical value.

HRW 9E (5th ed.). At what temperature do the following pairs of scales read the same: (a) Fahrenheit and Celsius, (b) Fahrenheit and Kelvin, and (c) Celsius and Kelvin?

The change in length for the rod is 20.11cm-20.05cm plus the expansion of the steel ruler at its 20.11cm mark:

∆Ls = Lss∆T = (20.11 cm)(11 x 10-6 /C˚)(270˚C-20˚C)= 0.055 cm

∆L = (20.11cm-20.05cm) + 0.055 cm= 0.115 cm

The coefficient of thermal expansion of the material the rodis made of is:

= ∆L/L∆T=23 x 10-6 /C˚ L LT

HRW 28P (5th ed.). At 20˚C, a rod is exactly 20.05 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270˚C, where the rod now measures 20.11 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made of?