Macroscopic Expressions of Molecular Adiabatic Compressibility of Methyl and Ethyl Caprate under High Pressure and High Temperature

The molecular compressibility, which is a macroscopic quantity to reveal the microcompressibility by additivity of molecular constitutions, is considered as a fixed value for specific organic liquids. In this study, we introduced two calculated expressions of molecular adiabatic compressibility to demonstrate its pressure and temperature dependency. The first one was developed from Wada’s constant expression based on experimental data of density and sound velocity. Secondly, by introducing the 2D fitting expressions and their partial derivative of pressure and temperature, molecular compressibility dependency was analyzed further, and a 3D fitting expression was obtained from the calculated data of the first one. The third was derived with introducing the pressure and temperature correction factors based on analogy to Lennard-Jones potential function and energy equipartition theorem. In wide range of temperatures<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mn>293</mml:mn><mml:mo>&lt;</mml:mo><mml:mtext>T</mml:mtext><mml:mo>/</mml:mo><mml:mtext>K</mml:mtext><mml:mo>&lt;</mml:mo><mml:mn>393</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and pressures<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mtext>P</mml:mtext><mml:mo>/</mml:mo><mml:mtext>MPa</mml:mtext><mml:mo>&lt;</mml:mo><mml:mn>210</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, which represent the typical values used in dynamic injection process for diesel engines, the calculated results consistency of three formulas demonstrated their effectiveness with the maximum 0.5384% OARD; meanwhile, the dependency on pressure and temperature of molecular compressibility was certified.