Chapter 9 Q43

[Ethan_Kato_1D]

The Answer in the solution manual states: "Assume no change in volume. To calculate the change in entropy for the hot and cold water, the amount of energy which flows from one to the other must first be calculated: q(c) = -q(h)." Why is that when there is no change in volume the heat of the cold water is equal to the negative heat of hot water?

[vsyacoubian2A]

The system can't be doing any work if you want to calculate free energy just using q. If a system is kept at constant volume, it can't do any work. That way, delta U =q.