Editing Coefficient of performance (section)

== Equation ==
The equation is:
:<math>{\rm COP} = \frac{|Q|}{ W}</math>
where
* <math> Q \ </math> is the useful [[heat]] supplied or removed by the considered system (machine).
* <math>W > 0\ </math> is the net [[Mechanical work|work]] put into the considered system in one cycle.

The COP for heating and cooling are different because the heat reservoir of interest is different. When one is interested in how well a machine cools, the COP is the ratio of the heat taken up from the cold reservoir to input work. However, for heating, the COP is the ratio of the magnitude of the heat given off to the hot reservoir (which is the heat taken up from the cold reservoir plus the input work) to the input work:
:<math> {\rm COP}_{\rm cooling}=\frac{|Q_{\rm C}|}{ W}=\frac{Q_{\rm C}}{ W}</math>

:<math> {\rm COP}_{\rm heating}=\frac{| Q_{\rm H}|}{ W}=\frac{Q_{\rm C} +  W}{ W} = {\rm COP}_{\rm cooling} + 1 </math>
where
*<math>  Q_{\rm C} > 0 \ </math> is the heat flow from the cold reservoir to the system; since heat is being extracted from the cold reservoir, this value is positive.
*<math>  Q_{\rm H} < 0 \ </math> is the heat flow from the hot reservoir to the system; since heat is being sunk into the hot reservoir, this value is negative.<ref name="PlanckBook">{{cite book |last=Planck |first=M. |title=Treatise on Thermodynamics |page=§90 & §137 |quote=eqs.(39), (40), & (65) |publisher=Dover Publications |year=1945}}.</ref> (see [[heat]]).

Note that the COP of a heat pump depends on its direction. The heat rejected to the hot sink is greater than the heat absorbed from the cold source, so the heating COP is greater by one than the cooling COP.