Thermodynamics of the low density excluded volume hadron gas

We consider thermodynamics of the 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 numbers 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 multi-component gases. The derivation is quite general as particles may have different sizes and shapes which can also depend on their momenta. Besides it's 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 the viral expansion, the validity limits of the low-density approximation are also discussed.