Comments on the modeling of hydrogen and hydrogen-containing mixtures with cubic equations of state

Many cubic equations of state have attractive terms that are products of a density function and a temperature function, the so-called alpha function. By making the alpha function substance-specific – usually by letting it depend on the acentric factor – reasonably good representations of the thermodynamic properties can be achieved for many substances. This approach, however, does not always work well for hydrogen and hydrogen-containing mixtures. It is shown in this work that, for hydrogen, an alpha function can be reasonably defined in the temperature range 30–300 K only, provided that the densities are not too high. For higher temperatures or for modeling liquid hydrogen it is necessary to introduce corrections for soft repulsion into the hard-sphere terms of the equations of state.