Statistical Physics

1.4 The Principle of Equal Probability 21Exercise 4. The internal energy of an ideal gas depends only on its temperature,and is independent of the volume V . Use this fact and the Boyle–Charleslaw to derive the relation between the constant-volume and constant-pressureheat capacities of an ideal gas, C P = C V + Nk B . (This relation is known asthe Mayer relation.)Exercise 5. The average velocity of a molecule of an ideal gas is given byv = √ 2k B T/m. Evaluate this velocity for an oxygen molecule in a gas at300 K. (One mole of oxygen molecules weighs about 32 g.)