http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html
η=1-Tc/Th =1- 253.15/323.15 =0.2166,
η = W/Qh =>
Qh= W/ η =3.6•10⁷/0.2166 = 1.66•10⁸ J= =39648.4 kCal
10 kW•h•10 ¢/kW•h= 100 ¢
(1.66•10⁸/1/055•10⁸)•88 ¢ = 55.05 ¢
100/55.05 = 1.82
(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50.0°C and a cold reservoir temperature of -20.0°C?
(b) How much heat in kilocalories would it pump into the warm environment if 3.60 multiplied by 107 J of work (10.0 kW·h) is put into it?
(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 88.0¢ per therm (a common unit of energy for natural gas), where a therm equals 1.055 multiplied by 108 J. Compare the cost of producing the same amount of heat by each method. (cost of heat pump / cost of natural gas)
a. Tc=253.15k, Th=323.15
COP=1/(1-253.15/323.15)=4.62
1 answer
1 answer