Thermodynamics of the low-density excluded-volume hadron gas

We consider the thermodynamics of excluded-volume particles at finite temperature and chemical potential in the low-density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure, and number of particles. We show that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multicomponent gases. The derivation is quite general, because particles may have different sizes and shapes which can also depend on their momenta. Besides its simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded-volume thermodynamics is the single-component gas of hard spheres. For this case, using a virial expansion, the validity limits of the low-density approximation are also discussed.