A Carnot engine operates between a hot reservoir at 600 K and a room at 300 K . The entire work output of this engine is used to drive a Carnot refrigerator that extracts heat from a cold storage at 200 K and rejects heat to the same room at 300 K . If the engine absorbs 1200 J of heat from the hot reservoir, the total heat rejected to the room by both the engine and the refrigerator combined is:

Step-by-step solution

First, calculate the efficiency of the Carnot engine: = 1 - T_ room T_ hot = 1 - 300 600 = 0.5 The work produced by the engine is: W = Q_ in = 0.5 1200 J = 600 J The heat rejected by the engine to the room is: Q_E = Q_ in - W = 1200 J - 600 J = 600 J Next, calculate the Coefficient of Performance (COP) of the Carnot refrigerator: = T_ cold T_ room - T_ cold = 200 300 - 200 = 2 The heat extracted from the cold storage by the refrigerator is: Q_C = W = 2 600 J = 1200 J The heat rejected by the refrigerator to the roo