Based on solutions of the Ornstein–Zernike equation (OZE) of Lennard–Jones potential for mean spherical approximation (MSA), we derive analytical formula for the compressibility assuming that the system is of low density, homogeneous, isotropic and composed of one component. Depending on this formula, we find the values of the bulk modulus and the compressibility of air at room temperature and the bulk modulus and the compressibility of Methane, Ethylene, Propylene and Propane at nine per ten of critical temperature of each hydrocarbon. Also, we find the speed of sound in the air at various temperatures, the speed of sound in each of Helium, Neon, Argon, Krypton, Xenon, Methane, Ethylene, Propylene, Propane, Hydrogen, Nitrogen, Fluorine, Chlorine, Oxygen, Nitrous oxide (laughing gas), Carbon dioxide, Nitric oxide, Carbon monoxide, Sulphur dioxide and dichlorodifluoromethane at room temperature. Besides, we find the speed of sound in Methane, Ethylene, Propylene and Propane at nine per ten of critical temperature of each hydrocarbons depending on the formula we find. We show that the simple formula we derive in this work is reliable and agrees with the results obtained from other studies and literatures. We believe it can be used for many systems which are in low densities and described by Lennard–Jones potential.

中文翻译：

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可压缩性公式，用于空气，稀有气体，某些碳氢化合物气体，某些双原子简单气体和某些其他流体。

基于Lennard-Jones平均球面近似（MSA）的Ornstein-Zernike方程（OZE）的解，我们假设系统为低密度，均质，各向同性且由一个组成部分组成，则得出可压缩性的解析公式。根据该公式，我们得出室温下空气的体积模量和可压缩性值，以及每种烃的临界温度十分之九时甲烷，乙烯，丙烯和丙烯的体积模量和可压缩性值。此外，我们还发现了在各种温度下空气中的声速，氦气，氖气，氩气，K气，氙气，甲烷，乙烯，丙烯，丙烷，丙烷，氢，氮，氟，氯，氧，一氧化二氮（笑气），二氧化碳，一氧化氮，一氧化碳，室温下的二氧化硫和二氯二氟甲烷。此外，根据找到的公式，我们发现甲烷，乙烯，丙烯和丙烷中每种烃的临界温度为十分之九时的声速。我们表明，在这项工作中得出的简单公式是可靠的，并且与从其他研究和文献中获得的结果一致。我们相信它可以用于许多低密度的系统，并由Lennard-Jones势描述。