A body of finite mass is originally at temperature T1, which is higher than that of a reservoir at temperature T2. Suppose an engine operates in a cycle between the body and the reservoir until it lowers the temperature of the body from T1 to T2, thus extracting heat Q from the body. If the engine does work W, then it will reject heat Q–W to the reservoir at T2. Applying the entropy principle, prove that the maximum work obtainable from the engine is
W (max) = Q – T2 (S1– S2)
Where S1– S2is the entropy decrease of the body.
If the body is maintained at constant volume having constant volume heat capacity Cv = 8.4 kJ/K which is independent of temperature, and if T1 = 373 K and T2 = 303 K, determine the maximum work obtainable.