KINETIC THEORY

I. In kinetic theory we try to link our description of the motion of atoms or molecules to measurable thermodynamic quantities.

A. Assumptions

1. Gas atoms are point masses

2. No forces act except during collisions

3. Collisions are elastic

II. Start with a single atom in a cubical box and look at the collisions with the walls. This a standard development in most texts and you should refer to the text at this point. The key point is that the root-mean-square speed (you should know how this is defined) can be related to the pressure and the density

vrms = [3p/(r)]1/2

A. From this point we can use pV=nRT to show that the average translation kinetic energy per atom is directly related to the temperature.

(1/2)m(vrms)2 = (3/2)kT

where k is Boltzmann's constant.

III. Since there are Avogadro's number of atoms in a mole of a gas, we find that the internal energy for our ideal monatomic gas is

Eint = (3/2)RT

A. What are the specific heat capacities for an ideal monatomic gas? Is the specific heat capacity the same for a constant pressure process and a constant volume process? Why or why not?

B. How does this idea that Eint is related to kinetic energy change if we have to deal with a diatomic molecule? What is Equipartition of Energy?