The efficiency of a reversible heat engine is given by the ratio of work output to heat input, which can be also be expressed in terms of the temperatures of the hot (TH) and cold (TC) reservoirs, η=1−‌
TC
TH
Given, efficiency is 50% 0.5=1−‌
TC
TH
Solving for ‌
TC
TH
, we get ‌
TC
TH
=0.5 Coefficient of performance (COP), COP=‌
QC
W
=‌
TC
TB−TC
For a reversible process, the (COP) can also be related to the temperatures of the hot and cold reservoirs, COP‌=‌
0.5×TH
TH−0.5×TH
‌=‌
0.5
1−0.5
=‌
0.5
0.5
=1 Therefore, the coefficient of performance of the refrigerator working between the same two temperature but reverse direction is 1 .
