  We have produced an interacting quantum degenerate Fermi gas of atoms
composed of two spin-states of magnetically trapped $^{40}$K. The relative
Fermi energies are adjusted by controlling the population in each spin-state.
Measurements of the thermodynamics reveal the resulting imbalance in the mean
energy per particle between the two species, which is as large as a factor of
1.4 at our lowest temperature. This imbalance of energy comes from a
suppression of collisions between atoms in the gas due to the Pauli exclusion
principle. Through measurements of the thermal relaxation rate we have directly
observed this Pauli blocking as a factor of two reduction in the effective
collision cross-section in the quantum degenerate regime.
