A thermodynamic engine operates cyclically and reversibly between two temperatur

Question

A thermodynamic engine operates cyclically and reversibly between two temperature reservoirs, absorbing heat from the high-temperature bath at 450 K and discharging heat to the low-temperature bath at 300 K.

a) what is the maximum theoretical thermodynamic efficiency of the engine?

b) Assuming the engine operates at the maximum theoretical efficiency, how much heat is discarded to the low-temperature bath if 1500 J of heat is absorbed from the high-temperature bath during each cycle?

c) At the maximum theoretical efficiency, how much work does the engine perform in one cycle of operation?

Explanation / Answer

a) Maximum thermodynamic efficiency

Efficiency = (Th - Tc)/Tc * 100 = (450-300)/300 * 100 = 50%

Hence the efficiency of the engine is equal to 50%

b)

Heat discarded = Total heat * (1 - efficiency)

=> 1500 J * (1 -50%) = 750J

Hence the heat discarded is equal to 750J

c)

Workdone in one cycle of operation

=> Heat * efficiency

=> 750 J

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