A Heat Pump

If you heat your home using electric heat, 1000 J of electrical energy can be transformed into 1000 J of heat. An alternate way of heating is to use a heat pump, which extracts heat from a lower-temperature region (outside the house) and transfers it to the higher-temperature region (inside the house). Let's say the work done in the process is 1000 J, and the temperatures are TH = 17°C = 290 K and TL = -23 °C = 250 K. What is the maximum amount of heat that can be transferred into the house?

  1. Something less than 1000 J (32/33) (97%)
  2. 1000 J (1/33) (3%)
  3. Something more than 1000 J (0/33) (0%)















The best we can do is determined by the Carnot relationship:
TL
TH
=
|QL|
|QH|
Therefore:     |QL| =
TL
TH
|QH|

Using this in the energy equation gives:
|QH| = |QL| + W =
TL
TH
|QH| + W
|QH| * ( 1 -
TL
TH
) = W
|QH| =
W TH
TH - TL

For our numerical example this gives:
|QH| =
1000 * 290
290 - 250
= 1000 * 7.25 = 7250 J

This is why heat pumps are much better than electric heaters. Instead of 1000 J of work going to 1000 J of heat we have 1000 J of work producing over 7000 J of heat.