Statistical entropy and a qualitative gas-liquid phase diagram

For a classical monatomic fluid, gas and liquid phases are differentiated on the basis of their statistical-mechanical entropy expressions. In the customary picture of a gas, each particle is first allowed to move independently over the entire volume; interactions are then introduced, and the configurational entropy becomes 1 minus the interaction corrections. In a liquid, the configurational entropy is assumed to be dominated by correlations, and is expressed as $S^{\mathrm{}\left(2\right)\mathrm{}}$ plus higher-order correlation corrections, where the two-particle term $S^{\mathrm{}\left(2\right)\mathrm{}}$ is of order -2. For liquid argon at 85 K on the saturation curve, $S^{\mathrm{}\left(2\right)\mathrm{}}$ is evaluated from the measured radial distribution function, and the entropy is accurately given by liquid statistical theory, with the higher-order correlation corrections being approximately 13% of the magnitude of $S^{\mathrm{}\left(2\right)\mathrm{}}$. A qualitative gas-liquid phase diagram is drawn for a classical monatomic fluid.