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College Physics (Urone)
Found in: Page 551

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Short Answer

What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of −25.0 ºC to a hot temperature of 40.0 ºC?

The heat pump’s performance coefficient is \(4.815\).

See the step by step solution

Step by Step Solution

Step 1: Introduction

The coefficient of performance is the ratio of power drawn from the pump to the power provided to the compressor.

Step 2:  Given parameters & formula for efficiency of heat engine and performance coefficient

The temperature of cold environment \({T_c} = - 25\;^\circ {\rm{C}} = 248\;{\rm{K}}\)

The temperature of cold reservoir \({T_h} = 40\;^\circ {\rm{C}} = 31{\rm{3}}\;{\rm{K}}\)

The efficiency of the Carnot engine \(\eta = 1 - \frac{{{T_c}}}{{{T_h}}}\)


\(\eta \) - efficiency of the engine.

\({T_c}\)- the temperature at which the cold reservoir is maintained.

\({T_h}\)- the temperature at which the hot reservoir is maintained.

\({\beta _{hp}}\) - heat pump’s performance coefficient.

Step 3:  Calculate efficiency and coefficient of performance of ideal heat pump

Maximum efficiency can be calculated by calculating Carnot efficiency as

\(\begin{aligned}{}\eta & = 1 - \frac{{{T_c}}}{{{T_h}}}\\ &= 1 - \frac{{248}}{{313}}\\ &= 0.2077\end{aligned}\)

Heat pump’s performance coefficient can be calculated as

\(\begin{aligned}{}{\beta _{hp}} &= 1/h \\ &= 1/0.2077\\ &= 4.815\end{aligned}\)

Therefore, the heat pump’s performance coefficient is \(4.815\) .

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