arXiv:2601.14345v1 Announce Type: new
Abstract: The attraction term in an equation of state for gases, $-a c^2$, proposed by Rankine in 1854, is generally related to the London dispersion force via a calculation of the second virial coefficient, $B_2$, by an equation $B_2 = 2pi N_0 int_0^infty left(1- exp left(omega / kTright)right) r^2 text{d}r$, where $omega$ is the potential of the attraction between two molecules in the gas. Here we present an alternative approach that does not use this equation, and does not a-priori assume that the function is quadratic in concentration, $c$. Still, the quadratic dependence on concentration is also found. We analyze a gas consisting of argon at temperatures between 200 and 700 K. From the numerical calculations, we derive that the attraction parameter depends on temperature according to a -1/6 power scaling, and thus the attraction component to the second virial coefficient, $B_2$, scales with a -7/6 power to temperature. For the same conditions, the virial equation presented above results in a square root scaling of $B_2$ with temperature, which is less accurate.