We theoretically investigate the specific heat CV at constant volume in the normal state of a p-wave interacting Fermi gas. Including fluctuations in the p-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how CV as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, CV is shown to be enhanced by p-wave pairing fluctuations, near the superfluid phase transition temperature Tc. Similar enhancement of CV(T ≃ Tc) is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of p-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the p-wave molecular Bose gas regime, and (3) the region between the two, where p-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a p-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above Tc.
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