Parametric Equations of State for Fluids near the Critical Point

Parametric equations of state near the critical point of fluids are discussed with emphasis on their physical implications and potential applications. Two specific phenomenological proposals in which the "distance" parameter is directly related to singular thermodynamic functions are studied. One of these is shown to be obtainable from a general equation of state in which the isothermal compressibility is used as a scaling factor. Both proposals are found to be in agreement with the $\mathrm{PVT}$ data on ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$. Consistency checks between $\mathrm{PVT}$ and specific-heat data on these fluids are made using the parametric equations.