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The sympathetic cooling of an initially degenerate Fermi gas by either anideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It isshown that the efficiency of cooling by a Bose gas below $T_c$ is by no meansreduced when its heat capacity becomes much less than that of the Fermi gas,where efficiency is measured by the decrease in the temperature of the Fermigas per number of particles evaporated from the coolant. This contradicts theintuitive idea that an efficient coolant must have a large heat capacity. Incontrast, for a Boltzmann gas a minimal value of the ratio of the heatcapacities is indeed necessary to achieve T=0 and all of the particles must beevaporated.Comment: 5 pages, 3 figure

Limits of sympathetic cooling of fermions: The role of heat capacity of the coolant