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Q37PE

Expert-verifiedFound in: Page 551

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 \(4.815\).

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

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.

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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