A Carnot engine works between two heat reservoirs at temperatures Th = 300 K and

Question

A Carnot engine works between two heat reservoirs at temperatures Th = 300 K and Tc = 85 K. (a) What is its efficiency? 71.7 Correct: Your answer is correct. % (b) If it absorbs 85 J from the hot reservoir during each cycle, how much work does it do? 60.92 Correct: Your answer is correct. J (c) How much heat does it give off in each cycle? 24.08 Correct: Your answer is correct. J (d) What is the coefficient of performance of this engine when it works as a refrigerator between these two reservoirs? 39.5 Incorrect: Your answer is incorrect.

Explanation / Answer

(a ) Efficiency = 1 – Tc /Th

Given Th = 300 k, Tc = 85 K

= 1 – 85/300 = 0.717 = 71.7 %

(b ) = W/QH , given QH = 85 J

So, work done W = 0.717×85 = 60.92 J

(c ) W = QH – QC

So, QC = 85 – 60.92 = 20.08 J

(d) Coefficient of performance = QC /W = 20.08/60.92 = 0.33 = 33 %

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