Calculate entropy change when the gases are identical

Question

Solve the following problem:

There are n₁ moles of an ideal monatomic gas at temperature T₁ and pressure P in one compartment of an insulated container. In an adjoining compartment separated by an insulating partition are ni moles of another ideal monatomic gas at temperature T₂ and pressure P. When the partition is removed:

(a) Show that the final pressure of the mixture is P.

(b) Calculate the entropy change when the gases are identical.

(c) Calculate the entropy change when the gases are different.