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 = 27°C = 300 K and Tc = -13 °C = 260 K. What is the maximum amount of heat that can be transferred into the house?
- Something less than 1000 J
- 1000 J
- Something more than 1000 J
The best we can do is determined by the Carnot relationship:
Tc
| |
Th
|
|
= |
|Qc|
| |
|Qh|
|
|
Therefore: |Qc| |
= |
Tc
| |
Th
|
|
|Qh| |
Using this in the energy equation gives:
|Qh| = |Qc| + W |
= |
Tc
| |
Th
|
|
|Qh| + W |
|Qh| * |
( |
1 - |
Tc
| |
Th
|
|
) |
= W |
|Qh| |
= |
W Th
| |
Th - Tc
|
|
For our numerical example this gives:
|Qh| |
= |
1000 * 300
| |
300 - 260
|
|
= 1000 * 7.5 = 7500 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 7500 J of heat.