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(a) What is the best coefficient of performance for a heat pump that has a hot r

ID: 2255985 • Letter: #

Question

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 44.0

What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 44.0degreeC and a cold reservoir temperature of -20.0degreeC? How much heat in kilocalories would it pump into the warm environment if 3.60 ? 107 J of work (10.0 kW·h) is put into it? Assume the cost of this work input is 10¢/kW·h. Also assume that the cost of direct production of heat by burning natural gas is 89.0¢ per therm (a common unit of energy for natural gas), where a therm equals 1.055 ? 108 J. Compare the cost of producing the same amount of heat by each method.

Explanation / Answer

The best coefficient of performance of the heat pump is given by = Thot/(Thot -tcold) = 317/(64) =4.9

The amount of heat that it would pump into the warm environment is COP * work = 4.9 * 3.6 * 10^7 * 0.239 cal = 42159.600Kcal

Since we are providiv 10 K W-h of work input . the cost of this work input in heat pump is 10 * 10 Kw-h = 100 ¢.

By direct production the cost to produce 3,6 * 10^7 J is (3.6*10^7)/(1.055*10^8) * 89 =30.369 ¢

cost of heat pump / cost of natural gas = 100/30.369 =3.29