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

`COP_(HP) = (1)/(\eta_(th))`

Step-by-step explanation:

The coefficient of performance of the reversible heat pump is:

`COP_(HP) = (T_(H))/(T_(H)-T_(C))`

`COP_(HP) = (1)/(1-(T_(C))/(T_(H)) )`

The thermal efficiency of the reversible power cycle is:

`\eta_(th) = 1 - (T_(C))/(T_(H))`

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

`COP_(HP) = (1)/(\eta_(th))`