To do a quick estimate of heat rejection of a refrigeration system, you could guess COP=3.

From that, Qe/(Qc-Qe) = 3
and therefore Qc = Qe (1 + 1/3)

The heat rejection factor = 1.3

But this is incorrect because the COP depends on the cyle temperatures.

The unknown is only the compressor efficiency.
Text book figures for Isentropic efficiency are 0.72 for a recip.

Surely this is not realistic? I would expect the same compressor with a very low suction to have a lower isentropic efficiency.

Has anybody seen a relationship for isentropic efficiency and pressure ratio?