Thermal Physics

1
Thermal Physics

• Ideal Gases
• Kinetic Theory of Gases

2
Ideal Gases Variables

• P is the pressure
• V is the volume
• T is the temperature (K)
• n is the amount of gas (moles)
• For low P (low densities) the gas is called ideal

• Avogadros Number, NA, is the number of particles
  per mole
• Chosen so that the mass of NA particles is equal
  to atomic mass

3
n and Equation of State

• Molar mass is the mass of one mole of substance
  (use periodic table, e.g. SiO2?60 g/mol)
• N is the number of molecules
• Equation of State
• Universal Gas Constant
• Boltzmanns Constant

4
Kinetic Theory Assumptions

• Large number of molecules average separation
  large compared to their size.
• Molecules obey Newtons Laws , but motion is
  random.
• Molecules interact elastically via short-range
  forces.
• Molecules make elastic collisions with the walls
  of the container.
• All molecules in a gas are identical.

5
Quantities Describing Gases

• State Variables describe the macroscopic state of
  the gas
• Pressure P
• Volume V
• Temperature T
• Microscopic Variables describe the individual
  molecules or atoms
• Mass m
• Velocity v

6
Connecting Macroscopic to Microscopic Pressure
d

• Use Impulse-Momentum
• Let ?t to be time for a round trip (1 collision
  with left wall for each round trip)

Fig. 10.14, p. 341
7
Connecting Macroscopic to Microscopic Pressure
(contd)

• Add contributions from all N molecules

• Average value of squared velocity is

Total force is
8
Connecting Macroscopic to Microscopic Pressure
(contd)

• Speed and the Pythagorean Theorem

• Since motion in each direction is completely
  random

Giving
9
Connecting Macroscopic to Microscopic Pressure
(contd)

• Total force is

• Divide by area A d 2 to find the pressure

10
Ideal Gas Law Revisited
Average translational kinetic energy per molecule
For monatomic gas
11
Root-Mean-Square Velocity

• Connects macroscopic to microscopic

• M is molar mass in kg/mol