(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 50.0°C and a cold reservoir temperature of -20.0°C?
4.61

(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?
39703.35 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 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.
(cost of heat pump / cost of natural gas)

I got the answers for ffirst two parts already, I only need help with part (c). Please show full work.

Explanation / Answer

(c)
1 kwh is equal to 3.6 * 10^6 J

Cost of direct production of Heat by Natural gas = 89.0 cents / (1.055*10^8)

Let us say heat Generated = 39703.35 kcal
Let us say heat Generated = 166118816.4 J

Cost of Direct production = [89.0 cents / (1.055*10^8)] * 166118816.4
Cost of Direct production = 140.138 cents
Cost of Direct production = 1.40$

Cost of production by Heat Pump = [10/( 3.6 * 10^6 )] *  (3.60 107)
Cost of production by Heat Pump = 100 Cents
Cost of production by Heat Pump = 1.0 $

cost of heat pump / cost of natural gas = 1.0/1.4
cost of heat pump / cost of natural gas = 0.714

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

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