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.

Figure 1

(a) The virial series from Eq. (38) truncated at $m=2,...,12$. The term $m=2$ corresponds to the lowest line. (b) The limiting values $z_{\lim }$ of $z$ for which the accuracy of $S_m\left(z\right)$ from Eq. (38) with $m=2,\cdots ,10$, relative to $S_{12}\left(z\right)$, is 2% (diamonds) and 10% (dots).

Figure 2

(a) Function $z(\sqrt{s},0.3)$ from Eq. (39) along the chemical freezeout line extracted from particle-yield data taken in central nucleus-nucleus collisions at different collision energies [1, 34]. (b) The limiting values of $R$ from Eq. (39) at $n=0.375{\mathrm{fm}}^{-3}$, for which the accuracy of the truncated series $S_m\left(z\right)$ for $m=2,\cdots ,10$, relative to $S_{12}\left(z\right)$, is 2% (diamonds) and $10\%$ (dots).