What is Slowly Leaking Box?

An ideal gas of atoms of number density at an absolute temperature is restricted to a thermally isolated container that has a small hole of area A in one of the walls. Assume a Maxwell velocity distribution for the atoms. The size of the hole is a lot smaller than the size of the container and much smaller than the mean free path of the atoms.

a) Evaluate the number of atoms arresting the wall of the container per unit area per unit time.  (Express your answer in terms of the signify velocity of the atoms.)

b) What is the ratio of the average kinetic energy of atoms departure the container to the average kinetic energy of atoms primarily occupying the container? Presume that there is no flow back to the container. Give a qualitative argument and calculate this ratio.

c) How much heat necessity you transfer to/from the container to keep the temperature of the gas constant?