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In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
It reads: = + [()] where is the number density, g(r) is the radial distribution function and () is the isothermal compressibility. Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation can be rewritten in the form:
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
Here =, the isothermal compressibility, is a measure of the relative increase of volume from an increase of pressure, at constant temperature, while =, the coefficient of thermal expansion, is a measure of the relative increase of volume from an increase of temperature, at constant pressure.
For a single component system, the "standard" three parameters are the isothermal compressibility , the specific heat at constant pressure , and the coefficient of thermal expansion . For example, the following equations are true:
Another measurable volumetric derivative is the isothermal compressibility, . This quantity can be related to derivatives of the excess molar volume, and thus the activity coefficients: This quantity can be related to derivatives of the excess molar volume, and thus the activity coefficients:
Since the isothermal compressibility is positive for nearly all phases, and the square of thermal expansion coefficient is always either a positive quantity or zero, the specific heat at constant pressure is nearly always greater than or equal to specific heat at constant volume: ,,.
The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure.