A box of volume \(V\) has a movable partition separating it into two compartments. The left compartment contains 3000 particles, the right one contains 1000 particles, and initially the partition is in the middle so that the compartments are of equal volume. The partition is released and slides horizontally until the system is in a new equilibrium state.

(a) In terms of \(V\), what is the volume of each compartment once the new equilibrium state is reached?

(b) What is the change in the system's entropy during this process?