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Found in: Page 551

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# 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 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 $$\eta = 1 - \frac{{{T_c}}}{{{T_h}}}$$

Here,

$$\eta$$ - 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 $$4.815$$ .