A Carnot cycle based ideal heat engine operates between two tanks each having same mass m of water. The source tank has an initial temperature of `T_(1) = 361 K` and the sink tank has an initial temperature of `T_(2) = 289 K`. Assume that the two tanks are isolated from the surrounding and exchange heat with the engine only. Specific heat of water is s.
(a) Find the final common temperature of the two tanks.
(b) Find the total work that the engine will be able to deliver by the time the two tanks reach common temperature.

Answer

(a) `T_(0)=sqrt(T_(1)T_(2))=323 K`
(b) W=ms `(T_(1)+T_(2)-2sqrt(T_(1)T_(2)) =4ms `