An engine runs between a reservoir at temperature 200   K and a hot body which is initially at temperature of 600   K . If the hot body cools down to a temperature of 400   K in the process, then the maximum amount of work that the engine can do (while working in a cycle) is (the heat capacity of the hot body is 1   J / K )

Step-by-step solution

η = W Q in  ⇒ W = η Q in Q = ∫ Cdt For maximum amount of work, efficiency should be maximum, means we have to assume carnot engine. ∴ η = 1 - T 2   T 1 = 1 - 200   T ∴ W = ∫ nQ in = - ∫ 600 400 1 - 200   T CdT = - C [ T - 200 ℓ n T ] 600 400 W = - C - 200 + ln 3 2 200 C = 1 (Given) W = 200 - 200 ln 3 2 W = 200 1 - ln 3 2