Two Carnot engines A and B operate in series such that engine A absorbs heat at T 1 and rejects heat to a sink at temperature T . Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T 3 . When workdone in both the cases is equal, to value of T is :

Step-by-step solution

W A = 1 - Q 2 Q 1 = 1 - T T 1 ⇒ Q 2 Q 1 = T T 1 W B = 1 - Q 3 Q 2 / 2 = 1 - T 3   T ⇒ 2 Q 3 Q 2 = T 3   T Now, W A = W B Q 1 - Q 2 = Q 2 2 - Q 3 ⇒ 2 Q 1 Q 2 + 2 Q 3 Q 2 = 3 ⇒ 2   T 1   T + T 3   T = 3 2   T 1 3 + T 3 3 = T