1. Lecture 11a Ideal gas Number of states and density of states
Partition functions q and Q
Thermodynamic Functions
Problem 12.9

2. Single molecule translational energy states
From quantum mechanics states of translational energy are enumerated by three integer numbers, l, m, n.
Number of states within radius R,
Number of states within energy 

3. Density of states Number of states with energy from 0 to 
Number of states with energy from  to  + d - g()d, where g() density of states

4. Partition function for translations qt - single particle
By definition
For a gas not close to T = 0, there is a huge number of states within a given energy range, thus the sum can be replaced with integral
With substitution the integration gives

5. Partition function Q - many particles
For indistinguishable particles

6. Thermodynamic functions
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7. Thermodynamic functions II

8. Problem 12.9
Determine the entropy change when two gases with number of moles N1 and N2, are initially in volumes V1 and V2 , such that
V2/ V1= N2/ N1, are allowed to mix in the combined volume
V1 + V2.