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

ID: 1471447 • Letter: #

Question

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 51.3°C and a cold reservoir temperature of 13.7°C? (b) How much heat in kilocalories would it pump into the warm environment if 3.60 x107 J of work (10.0 kW · h) is put into it? kcal (c) 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 79.0¢ 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 as a ratio: cost of heat pump/cost of natural gas.

Explanation / Answer

a) Tc=259.3 K, Th=324.3 K
COP=1/(1-259.3/324.3)=4.99

b) =1-Tc/Th =1- 259.3/324.3 =0.2004,
= W/Qh =>
Qh= W/ =3.6•10/0.2004 = 1.796•10 J= 42966.5 kCal


c) 10 kW•h•10 ¢/kW•h= 100 ¢
(1.055•10/1.796•10)•79 ¢ = 46.41 ¢
100/46.41 = 2.15