Linear Relation of Temperature and Density at Unit Compressibility Factor

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Abstract
A linear relation is found for the experimental temperatures and densities at which the compressibility factor PV/RT equals unity. The two characteristic constants of the relation are evaluated for 12 gases for which appropriate data exist. The pertinent range of temperature and density for gases is from the critical temperature to the Boyle temperature, and from zero density to over twice the critical density. For one gas, Ar, the available data extend over this entire range and fit the linear law to within two parts per thousand. For CH4, Xe, and C2H4 over shorter ranges, the data are linear to within a few parts in ten thousand. Implications of the relation are discussed, including its usefulness as a necessary condition for equations of state, as a basis for a corresponding states treatment, as a means for detecting and correcting experimental errors in PVT measurements, and in providing a possible insight into the nature of intermolecular forces.