Question

Two reversible cycles operate between hot and cold reservoirs at temperature TH and TC, respectively. If one is a power cycle and the other is a heat pump cycle, what is the relation between the coefficient of performance of the heat pump cycle and the thermal efficiency of the power cycle?

Answer 1

Answer:

$COP_{HP} = \frac{1}{\eta_{th}}$

Explanation:

The coefficient of performance of the reversible heat pump is:

$COP_{HP} = \frac{T_{H}}{T_{H}-T_{C}}$

$COP_{HP} = \frac{1}{1-\frac{T_{C}}{T_{H}} }$

The thermal efficiency of the reversible power cycle is:

$\eta_{th} = 1 - \frac{T_{C}}{T_{H}}$

After a quick comparison between both expressions, the following relation is found:

$COP_{HP} = \frac{1}{\eta_{th}}$