Classical Gases

Ideal gas

Equipartition Theorem

Each independent square, average value equals to

Diatomic gas

Define:

• 
  
• 
  
• $H_{rot}=\sum_{i=1}^{N} \frac{\vec{L}{i}^{2}}{2I}$\varepsilon{rot}=k_{B}T,\ C_{rot}=k_{B}$$

So:

However, successive freezing of vibration and rotation modes!
Quantum effect at temperature ~ K

Vibration

Partition function:


Heat capacity:

Define characteristic temperature:

• High temperature limit:
  
• Low temperature limit:
  

Rotation

Partition function:

Define characteristic temperature:

• High temperature limit:
  
  $$Z\approx \int {0}^{\infty} e^{ - \frac{\theta{rot}}{T}x }, dx=\frac{T}{\theta rot} \implies C_{rot}=k_{B}$$
• Low temperature limit:
  
  

Interacting gases

Virial Expension: (expension in small parameter n)

Compute :