What is the best coefficient of performance for a heat pump that has a hot reser

Question

What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 42.0 degrees C and a cold reservoir temperature of -20.0 degrees C ? (Answer is 5.08)

How much heat in kilocalories would it pump into the warm environment if 3.60 x 10^7 J of work (10.0 kW.h) is put into it?

Assume the cost of this work input is 10 cents/kW.h. Also assume that the cost of direct production of heat by burning natural gas is 90.0 cents per therm (a common unit of energy for natural gas), where a therm equals 1.055 x 10^8 J. Compare the cost of producing the same amount of heat by each method (cost of heat pump/cost of natural gas).

Explanation / Answer

What is the coefficient of performance of a Carnot heat pump operating between these temperatures?
The Carnot efficiency is:
change to Kelvin temperatures

[T(hot) -T(cold)] / T(hot) x 100%=

[315.15 - 267.15] / (315.15) x100% = 15.23%

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