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# Science Fair Project Encyclopedia

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# Heat pump

A heat pump is a machine which moves heat from a low temperature reservoir to a higher temperature reservoir under supply of work.

Common examples are:

Heat pumps are realized through several physical effects, but they are classified depending on their applications (driving energy, source and sink of heat, or a heat pump which is basically a refrigeration machine). Refrigerators, air conditioners and heating systems are all common applications of heat pumps.

An easy way to imagine how a heat pump works is to imagine the heat in a given space - say the volume of a football (a soccerball for those in the USA). The air within the volume of the football has say 100 units of heat. This air is then compressed to the size of ping pong ball (table tennis ball for affectionados); it still contains the same 100 units of heat, but the heat is much more concentrated and thus the average heat per volume unit is much higher. The ping pong volume of heat is then moved from the heat source area to the target area that has a lower per volume concentration of heat. Since the heat of the ping pong ball volume is now a higher concentration than the surrounding heat, the heat is given off until the ping pong ball volume heat reaches the same concentration of heat as the surrounding area. The ping pong ball volume is then moved outside the target area back to the heat source area and allowed to expand. In expanding the heat per unit volume of the football is now much lower than the source and the football volume absorbs heat from the surrounding area. The process then repeats.

When comparing the performance of heat pumps, it is best to avoid the word "efficiency", as it has many different meanings. The term coefficient of performance or COP is used to describe the ratio of heat output to electrical power consumption. A typical heat pump has a COP of about three, whereas a typical electric heater has a COP of one.

The COP of a heatpump is restricted by the second law of thermodynamics.

$COP_{\mathrm{heating}} = \frac{\Delta Q_{\mathrm{hot}}}{\Delta A} \leq \frac{T_{\mathrm{hot}}}{T_{\mathrm{hot}}-T_{\mathrm{cool}}} = \frac{1}{\eta_{\mathrm{carnotcycle}}}$
$COP_{\mathrm{cooling}} = \frac{\Delta Q_{\mathrm{cool}}}{\Delta A} \leq \frac{T_{\mathrm{cool}}}{T_{\mathrm{hot}}-T_{\mathrm{cool}}}$

All temperatures T are measured in kelvins.