The so-called characteristic curves of Brown-the Amagat (Joule inversion), Boyle, and Charles (Joule-Thomson inversion) curves-of hydrogen are calculated with several equations of state. This work demonstrates that not all equations can generate physically reasonable Amagat curves. After inclusion of corrections for soft repulsion (based on the Weeks-Chandler-Andersen perturbation theory) and quantum effects into the simplified perturbed-hard-chain theory (SPHCT) equation of state, this equation is able to not only generate an Amagat curve, but also predict pVT data, residual Gibbs energies, and heat capacities of several gases at and above 100 MPa reasonably well. List of symbolsA Helmholtz energy B 2nd virial coefficient C p Isobaric heat capacity C V Isochoric heat capacity c Chain length parameter of the SPHCT EOS d Apparent hard-sphere diameter d 0 d at zero density H Enthalpy