Question

Derive an expression for the partition function of an ideal monoatomic gas. Hence obtain an expression for its entropy.

Answer 1

The dispersion ratio of ultrarelativistic particles has the form

partition function of a monatomic classical gas

Using standard thermodynamic relations, we obtain equations of state

$$c_v=3, p=\frac{\theta}{v}$$

$$c_p=c_v+1=4$$

Due to the thermal equation of state of an ideal gas p = θ / v and cv = const, the equation of the adiabatic process has the form

$$pv^\gamma=const$$

where

$$\gamma=\frac{c_p}{c_v}=\frac{4}{3}$$