Question

Account for the temperature and volume dependence of the entropy of a perfect gas in terms of Boltzmann distributions.

Answer 1

A molecule moving through a gas collides with other molecules in a random fashion

This behavior is sometimes referred to as a random-walk process

The mean free path increases as the number of molecules per unit volume decreases

The mean free path, l , equals the average distance vt traveled in a time interval t divided by the number of collisions that occur in that time interval: The number of collisions per unit time is the collision frequency: The inverse of the collision frequency is the collision mean free time l = vt d2 ( ) vt nv = 1 d2N/V

The distribution of molecular speeds depends both on the mass and on temperature