A partition divides a container into two equal compartments, A and B. Initially compartment A contains a gas of distinguishable particles and compartment B is empty.

(a) What is the change in the entropy of the gas if the partition is removed and the gas is allowed to expand into the volume \(V\) of the container?

(b) If the partition is reinserted after the gas has reached equilibrium in the volume \(V\), what is the change in the entropy of the gas due to the reinsertion?