As in a fermi gas all fermions can't occupy the same quantum state.Therefore if a fermi gas reaches 0 Kelvin only a single fermion will occupy zero energy state,other fermions will have some kinetic energy.Also as the temperature of a body is because of the virtue of the motion of the particles constituting the body,the fermi gas should have a temperature.This contradicts our earlier assumption that the fermi gas is at 0 Kelvin!
Hence,can a fermi gas ever reach 0 Kelvin?
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