Question

A vessel filled with gas is divided into two equal parts 1 and 2 by a thin heat-insulating partition with two holes. One hole has a small diameter, and the other has a very large diameter (in comparison with the mean free path of molecules). In part 2 the gas is kept at a temperature η times higher than that of part 1. How will the concentration of molecules in part 2 change and how many times after the large hole is closed?

Answer 1

If the temperature of the compartment 2 is η times more than that of compartment 1, it must contain 1/η times less number of molecules since pressure must be the same when the big hole is open. If M - mass of the gas in 1 than the mass of the gas in 2 must be M/η . So immediately after the big hole is closed.

where m = mass of each molecule and n⁰₁, n⁰₂  are concentrations in 1 and 2. After the big hole is closed the pressures will differ and concentration will become n₁ and n₂ where