1. Temperature and Kinetic Theory
Chapter 10
Temperature and Kinetic Theory

2. Definitions
Temperature – a measure of the average kinetic energy of the the molecules making up a substance, measured in [C] or [F] or [K].
Internal Energy (thermal energy) the combined kinetic and potential energy of the molecules of a substance measured in [Joules].
Heat – the transfer of thermal energy measured in [Joules].

3. Internal Energy Kinetic energy – when molecules are in motion
Potential energy – when molecules have stored energy

4. Fahrenheit and Celsius Scales
Use two points to find the equation…

5. Fahrenheit, Celsius and Kelvin Scales
F = 9/5 C + 32
C = 5/9(F – 32)
K = C + 273

6. Ideal Gas Law PV = nRT P = Pressure V = Volume n = number of moles
R = univ. gas constant (8.31 J/mol ºK)
T = Temperature in Kelvin

7. Things to Know
A mole of a substance is a quantity containing 6.02 X 1023 molecules
Standard Temperature and Pressure means p = 1 atm = 1.01 X 105 Pa,
T = 0ºC = 273 K
Formula weight in Grams = 1 mole
Must use Kelvin for temperature!

8. Special Cases of Ideal Gas Law
If the number of molecules (mass) doesn’t change:
Constant Temperature, then p1V1 = p2V2
Constant Pressure , then V1/T1 = V2/T2
Constant Volume, then p1/T1 = p2/t2

9. Examples
A low density gas in a rigid container is initially at 20ºC and a particular pressure, p1. If the gas is heated to 60ºC, by what factor does pressure change?

10. Examples
The weather report gives the day’s high temperature as 10ºC and predicts the next day’s high temperature as 20ºC. A father tells his son that this means it will be twice as warm tomorrow, but the son says it does not mean that. Do you agree with the father or the son?

11. Thermal Expansion
Solids and liquids expand or contract with changes in temperature.
Space between molecules becomes greater or less as temperature changes.
ΔL = αL0ΔT ; L0= original length
α = thermal coefficient of
linear expansion

12. Example
A steel beam is 5.0 m long at 20ºC. On a hot day, the temperature rises to 40ºC. What is the change in the beam’s length? α = 12 X 10-6 C-1

13. Area and Volume Expansion
ΔA = 2αA0ΔT Area Expands with Temperature
ΔV = 3αV0ΔT Volume Expands with Temperature

14. Macroscopic vs Microscopic Ideal Gas Law
pV = nRT R = 8.31 J/mol K
n = # of moles
Microscopic
pV = NkbT kb = 1.38 X J/K
N = # of molecules

15. Kinetic Theory for Monatomic Gases
Monatomic – single atom gases.
Diatomic – molecules contain 2 atoms.
Monatomic gases are easy to study because atoms move without rotation or vibration
Monatomic gases obey the laws of mechanics (recall for elastic collisions we apply Conservation of Momentum and Conservation of Energy)

16. Kinetic Theory for Monatomic Gases
Molecules (atoms) undergo perfectly elastic collisions with the walls of the container.
We assume molecules are separated by large enough distances so that molecular collisions can be neglected.
Then…
pV = 1/3 Nmv2rms
N = # of molecules
m = mass of molecule
vrms = average speed of molecule

17. Math… pV = 1/3 Nmv2rms = NkbT So ½ mv2rms = 3/2 kbT
Or 3/2 kbT = ½ mv2rms
What does this mean?
Temperature is proportional to average KE!

18. Example
Find the average speed (v2rms) of a Helium atom in a 20ºC balloon at room temperature. Assume
mHe = 6.65 X kg

19. Summary- Kinetic Theory for Monatomic Ideal Gas
Average Kinetic Energy
KEav = ½ m vrms2 = 3/2 kbT
kb = 1.38 X J/K
Total Internal Energy
U = 3/2 NkbT = 3/2 nRT