Heat Pump COP

#457 / Thermo Easy

An air-to-air heat pump operates between -10°C on the cold side and 45°C on the hot side. What is the max theoretical efficiency?

Expand Hint

For a Carnot heat pump cycle, the Coefficient of Performance (COP) is:

$$$COP_c=\frac{T_H}{(T_H-T_L)}$$$

where $$T_H$$ and $$T_L$$ are the absolute high and low temperatures respectively in either Kelvin or Rankine.

Hint 2

To convert Celsius to Kelvin:

$$$K\:=\:^{\circ}C+273$$$

For a Carnot heat pump cycle, the Coefficient of Performance (COP) is:

$$$COP_c=\frac{T_H}{(T_H-T_L)}$$$

where $$T_H$$ and $$T_L$$ are the absolute high and low temperatures respectively in either Kelvin or Rankine. To convert Celsius to Kelvin:

$$$K=\:^{\circ}C+273$$$

Thus, the high and low temperatures are:

$$$K_H=45^{\circ}C+273=318\:K$$$

$$$K_L=-10^{\circ}C+273=263\:K$$$

Finally,

$$$COP_c=\frac{318K}{(318K-263K)}=\frac{318}{55}=5.78$$$

5.78

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