Thermodynamic Properties of Liquids from Speed of Sound Measurements

A strategy for deriving thermodynamic properties of liquids (</span></span><span style="font-family: Symbol, serif;"><span style="font-size: x-small;"><span lang="en-US"><em>r</em></span></span></span><span style="font-size: x-small;"><span lang="en-US">, </span></span><span style="font-size: x-small;"><span lang="en-US"><em>c</em></span></span>_{<span style="font-size: x-small;"><span lang="en-US"><em>p</em></span></span>}<span style="font-size: x-small;"><span lang="en-US">, </span></span><span style="font-size: x-small;"><span lang="en-US"><em>c</em></span></span>_{<span style="font-size: x-small;"><span lang="en-US"><em>v</em></span></span>}<span style="font-size: x-small;"><span lang="en-US">) from speed of sound is presented. It is based on numerical integration of differential equations connecting speed of sound with other thermodynamic properties. Two different procedures are recommended: One for liquids with lower and moderate critical pressures (LMCP), and another for liquids with higher critical pressures (HCP). The set of differential equations is solved as the initial value problem in both cases. However, for LMCP liquids initial conditions (several accurate values of </span></span><span style="font-family: Symbol, serif;"><span style="font-size: x-small;"><span lang="en-US"><em>r</em></span></span></span><span style="font-size: x-small;"><span lang="en-US"> and </span></span><span style="font-size: x-small;"><span lang="en-US"><em>c</em></span></span>_{<span style="font-size: x-small;"><span lang="en-US"><em>p</em></span></span>}<span style="font-size: x-small;"><span lang="en-US">) are specified along isobar near the critical pressure, and for HCP liquids along the liquid-vapor saturation curve. The procedures are tested on ethane, carbon dioxide, and water