Exercise 5.1. A perfect gas containing a single species of molecular weight M^ is enclosed in a container at equilibrium at pressure p and temperature T. The gas escapes into vacuum through a small circular hole of area A in the wall of the container. Assume the following ideal conditions: (1) The wall of the container is negligibly thick and is planar in the vicinity of the hole. (2) The diameter of the hole is appreciably smaller than the mean free path, but considerably larger than the molecular diameter. (a) Show that the number of molecules escaping from the hole per unit area per unit time is given by nC/4. (b) Obtain an expression for the rate of mass outflow in terms of (and only of) p,T,M^,A, and R^. (c) Show that the mean kinetic energy of the escaping molecules is greater than that of the molecules inside the container in the ratio 4/3. Can you give a physical explanation of this result