# 9.5 Applications of thermodynamics: heat pumps and refrigerators  (Page 2/7)

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The electrically driven compressor (work input $W$ ) raises the temperature and pressure of the gas and forces it into the condenser coils that are inside the heated space. Because the temperature of the gas is higher than the temperature inside the room, heat transfer to the room occurs and the gas condenses to a liquid. The liquid then flows back through a pressure-reducing valve to the outdoor evaporator coils, being cooled through expansion. (In a cooling cycle, the evaporator and condenser coils exchange roles and the flow direction of the fluid is reversed.)

The quality of a heat pump is judged by how much heat transfer ${Q}_{\text{h}}$ occurs into the warm space compared with how much work input $W$ is required. In the spirit of taking the ratio of what you get to what you spend, we define a heat pump’s coefficient of performance ( ${\text{COP}}_{\text{hp}}$ ) to be

${\text{COP}}_{\text{hp}}=\frac{{Q}_{\text{h}}}{W}\text{.}$

Since the efficiency of a heat engine is $\text{Eff}=W/{Q}_{\text{h}}$ , we see that ${\text{COP}}_{\text{hp}}=1/\text{Eff}$ , an important and interesting fact. First, since the efficiency of any heat engine is less than 1, it means that ${\text{COP}}_{\text{hp}}$ is always greater than 1—that is, a heat pump always has more heat transfer ${Q}_{\text{h}}$ than work put into it. Second, it means that heat pumps work best when temperature differences are small. The efficiency of a perfect, or Carnot, engine is ${\text{Eff}}_{\text{C}}=1-\left({T}_{\text{c}}/{T}_{\text{h}}\right)$ ; thus, the smaller the temperature difference, the smaller the efficiency and the greater the ${\text{COP}}_{\text{hp}}$ (because ${\text{COP}}_{\text{hp}}=1/\text{Eff}$ ). In other words, heat pumps do not work as well in very cold climates as they do in more moderate climates.

Friction and other irreversible processes reduce heat engine efficiency, but they do not benefit the operation of a heat pump—instead, they reduce the work input by converting part of it to heat transfer back into the cold reservoir before it gets into the heat pump.