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 )

Question

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 ), 200 ( 1 - ln 2 ) J, 200 ( 1 - ln 3 / 2 ) J, 200 ( 1 + ln 3 / 2 ) J, 200 J

MARKS App · Accepted Answer

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

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