**1. **Kinetic Theory of Gases
Physics 202
Professor Lee Carkner
Lecture 13

**2. **What is a Gas?
But where do pressure and temperature come from?
A gas is made up of molecules (or atoms)
The pressure is a measure of the force the molecules exert when bouncing off a surface
We need to know something about the microscopic properties of a gas to understand its behavior

**3. **Mole A gas is composed of molecules
m =
N =
When thinking about molecules it sometimes is helpful to use the mole
1 mol = 6.02 X 1023 molecules
6.02 x 1023 is called Avogadro?s number (NA)
M =
M = mNA
A mole of any gas occupies about the same volume

**4. **Ideal Gas Specifically, 1 mole of any gas held at constant temperature and constant volume will have almost the same pressure
Gases that obey this relation are called ideal gases
A fairly good approximation to real gases

**5. **Ideal Gas Law The temperature, pressure and volume of an ideal gas is given by:
pV = nRT
Where:
R is the gas constant 8.31 J/mol K
V in cubic meters

**6. **Work and the Ideal Gas Law
p=nRT (1/V)

**7. **Isothermal Process
If we hold the temperature constant in the work equation:
W = nRT ln(Vf/Vi)
Work for ideal gas in isothermal process

**8. **Isotherms From the ideal gas law we can get an expression for the temperature
For an isothermal process temperature is constant so:
If P goes up, V must go down
Lines of constant temperature
One distinct line for each temperature

**9. **Constant Volume or Pressure
W=0
W = ?pdV = p(Vf-Vi)
W = pDV
For situations where T, V or P are not constant, we must solve the integral
The above equations are not universal

**10. **Gas Speed
The molecules bounce around inside a box and exert a pressure on the walls via collisions
The pressure is a force and so is related to velocity by Newton?s second law F=d(mv)/dt
The rate of momentum transfer depends on volume
The final result is:
p = (nMv2rms)/(3V)
Where M is the molar mass (mass of 1 mole)

**11. **RMS Speed
There is a range of velocities given by the Maxwellian velocity distribution
We take as a typical value the root-mean-squared velocity (vrms)
We can find an expression for vrms from the pressure and ideal gas equations
vrms = (3RT/M)?
For a given type of gas, velocity depends only on temperature

**12. **Maxwell?sDistribution

**13. **Translational Kinetic Energy
Using the rms speed yields:
Kave = ?mvrms2
Kave = (3/2)kT
Where k = (R/NA) = 1.38 X 10-23 J/K and is called the Boltzmann constant
Temperature is a measure of the average kinetic energy of a gas

**14. **Maxwellian Distribution and the Sun
The vrms of protons is not large enough for them to combine in hydrogen fusion
There are enough protons in the high-speed tail of the distribution for fusion to occur

**15. **Next Time Read: 19.8-19.11