Calculate the change of entropy
((a)) of a bath containing water, initially at 20∘C, when it is placed in thermal contact with a very large heat reservoir at 80∘C,
((b)) of the reservoir when process (a) occurs,
((c)) of the bath and of the reservoir if the bath is brought to 80∘C through the operation of a Carnot engine between them.
The bath and its contents have total heat capacity 104 J K−1.
[Hint for (c): which of the heat transfers considered in parts (a) and (b) change when you use a Carnot engine, and by how much? Where does the difference in heat energy go?]