Find COP of a reversible heat pump operating between temperatures 20 and 200 °c

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Problem Statement: 

Calculate the Coefficient of Performance (COP) of a reversible heat pump operating between temperatures 20°C and 200°C.

### Explanation:

The Coefficient of Performance (COP) of a heat pump is a measure of its efficiency, defined as the ratio of the heat delivered to the work input. For a reversible heat pump, the COP can be calculated using the temperatures of the hot and cold reservoirs.

Given:
- Temperature of the cold reservoir (T_cold) = 20°C = 293 K 
- Temperature of the hot reservoir (T_hot) = 200°C = 473 K 

The formula for COP of a heat pump is:
\[
\text{COP} = \frac{T_{\text{hot}}}{T_{\text{hot}} - T_{\text{cold}}}
\]

### Calculation:

Substitute the given temperatures (in Kelvin) into the formula:
\[
\text{COP} = \frac{473}{473 - 293} = \frac{473}{180} \approx 2.63
\]

### Conclusion:

The Coefficient of Performance (COP) of the reversible heat pump operating between temperatures 20°C and 200°C is approximately 2.63.
Transcribed Image Text:### Problem Statement: Calculate the Coefficient of Performance (COP) of a reversible heat pump operating between temperatures 20°C and 200°C. ### Explanation: The Coefficient of Performance (COP) of a heat pump is a measure of its efficiency, defined as the ratio of the heat delivered to the work input. For a reversible heat pump, the COP can be calculated using the temperatures of the hot and cold reservoirs. Given: - Temperature of the cold reservoir (T_cold) = 20°C = 293 K - Temperature of the hot reservoir (T_hot) = 200°C = 473 K The formula for COP of a heat pump is: \[ \text{COP} = \frac{T_{\text{hot}}}{T_{\text{hot}} - T_{\text{cold}}} \] ### Calculation: Substitute the given temperatures (in Kelvin) into the formula: \[ \text{COP} = \frac{473}{473 - 293} = \frac{473}{180} \approx 2.63 \] ### Conclusion: The Coefficient of Performance (COP) of the reversible heat pump operating between temperatures 20°C and 200°C is approximately 2.63.
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