A problem from my textbook mentions a refrigerator working with $35\,\%$ efficiency. I thought that in this case the coefficient of performance (COP) was used, specifically $Q_\mathrm{cold}/W,$ which is different from the COP of a heat pump.

Let's say it refers to $W/Q_\mathrm{hot} = 0.35,$ but the refrigerator works between two reservoirs: one at $\pu{0 °C}$ and the other at $\pu{20 °C}.$ If we use the temperature ratio for efficiency, it can't be above $35\,\%.$

So, what does $35\,\%$ refer to? Does it refer to $35\,\%$ of the maximum efficiency?

  • $\begingroup$ @ToddMinehardt Hmm, for thermal pumps like refrigerators, is not the thermal efficiency rather $\eta = \frac{Q_\mathrm{in}}{Q_\mathrm{out}}$ ? With $\lim_{T_1 \rightarrow T_2}{(Q_\mathrm{in})}=Q_\mathrm{out}$ for the ideal Carnot-like case? Your efficiency seems to me rather for heat engines which have rather complementary efficiency to the one of heat pumps. $\endgroup$
    – Poutnik
    Commented Nov 17, 2021 at 9:13
  • $\begingroup$ P.S.: Like $\eta_\mathrm{pump} + \eta_\mathrm{engine} = 1$ for the same $T$ range and Carnot-like cycles. $\endgroup$
    – Poutnik
    Commented Nov 17, 2021 at 10:36


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