Answer:
[tex]COP_{HP} = \frac{1}{\eta_{th}}[/tex]
Explanation:
The coefficient of performance of the reversible heat pump is:
[tex]COP_{HP} = \frac{T_{H}}{T_{H}-T_{C}}[/tex]
[tex]COP_{HP} = \frac{1}{1-\frac{T_{C}}{T_{H}} }[/tex]
The thermal efficiency of the reversible power cycle is:
[tex]\eta_{th} = 1 - \frac{T_{C}}{T_{H}}[/tex]
After a quick comparison between both expressions, the following relation is found:
[tex]COP_{HP} = \frac{1}{\eta_{th}}[/tex]
