Conceptual Physics

limits the maximum COP is shown in Equation 2 on the right. The right side of the

inequality is the ratio of the hot reservoir temperature to the difference of the hot and

cold temperatures. A Carnot engine operating “in reverse” as a heat pump achieves the

maximum COP. That is, the equality holds.

In Example 1, the maximum COP is calculated for a heat pump operating to warm a

house, with an indoor temperature of 21°C (about 70°F) and an outdoor temperature

of13°C (about 55°F). The theoretical maximum COP is 37; the actual operating COP

would be less. Typical COPs for heat pumps range from about five to 10. A heat pump

with a COP of five would transfer five joules of thermal energy for every joule of work

supplied.

A refrigerator acts something like a heat pump, but its purpose is to cool the cold

reservoir, the refrigerator’s interior. The coefficient of performance of refrigerators is

sometimes measured as Qc/W. Again, this is the ratio of “what you want” (cooling the

cold reservoir) to “what you pay” (work done). For refrigerators, COP values from four

to six are typical.

MaximumCOP

Th = hot reservoir temperature (K)

Tc = cold reservoir temperature (K)

What is the maximum COP of a

heat pump operating between

these indoor and outdoor

temperatures?

Th = 21 + 273.15 K = 294 K

Tc = 13 + 273.15 K = 286 K

COPmax = 37

21.11 - Sample problem: heat pump in action

If you heat a house using an electric furnace, the electric energy supplied to the furnace is converted into thermal energy and transferred to the

air inside the house, increasing its temperature. If the furnace is supplied with 1250 joules of electrical energy, it can increase the energy of the

air by at most 1250 J. It will be interesting to contrast this value with the amount of heat that a heat pump can cause to flow into the house

For these temperatures, what is the

maximum COP for a heat pump? If

the COP of a heat pump is 5.48, and

1250 J of work is done on it, how

much heat energy could it maximally

transfer inside from the outdoors?

(^394) Copyright 2007 Kinetic Books Co. Chapter 21