One of the formulations of the third laws of thermodynamics is that a processes become more isentropic as
one approaches the absolute zero temperatures. We examine this prediction by studying an operating model
of a quantum refrigerator pumping heat from a cold to a hot reservoir. The working medium consists of a
gas of noninteracting harmonic oscillators. The model can be solved in closed form in the quasi-static limit
or numerically for general conditions. It is found that the isentropic limit for <i>T<sub>c</sub></i> → 0 is approached only on
the expansion segment of the refrigeration cycle. The scaling of the cooling rate with temperature is shown to
be consistent with the second law of thermodynamics. This scaling is also consistent with the unattainability
principle which is an alternative formulation of the third law of thermodynamics.