Response to the following problem:
There are n1 moles of an ideal gas at pressure P1 and temperature T in one compartment of an insulated container. In an adjoining compartment separated by a partition are n: moles of an ideal gas at pressure P2 and temperature T. When the partition is removed:
(a) Calculate the final pressure of the mixture.
(b) Calculate the entropy change when the gases are identical.
(c) Calculate the entropy change when the gases are different.
(d) Prove that the entropy change in part (c) is the same as that which would be produced by two independent free expansions.