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

Question

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 56.0°C and a cold reservoir temperature of -22.0°C? (b) 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? 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 87.0¢ 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. (cost of heat pump / cost of natural gas)

Explanation / Answer

a)

given

Tc = -22 C = -22 + 273 = 251 K

Th = 56 C = 56 + 273 = 329 k

we know,
Coefficient of performance, COP = Tc/(Th - Tc)

= 251/(329 - 251)

= 3.218 <<<<<<---------Aswer

b)

now Apply, COP = Qc/Workdone by refregerator

COP = QC/W

Qc = COP*W

= 3.218*3.6*10^7

= 1.158*10^8 J

now Apply,

QH - Qc = W

==> Qh = W + QC

= 3.6*10^7 + 1.158*10^8

= 1.518*10^8 J <<<<<<<-----------Answer

c)

cost of heat pump = (1.518*10^8/(3.6*10^6))*10

= 421.7 cents

cost of natural gas = (1.518*10^8/(1.055*10^8))*87

= 125.2

cost of heat pump / cost of natural gas = 421.7/125.2

= 3.368 <<<<<<<-----------Answer

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.