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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.
The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure. Moreover, considering derivatives such as ∂ 3 G ∂ P ∂ T 2 {\displaystyle {\frac {\partial ^{3}G}{\partial P\partial T^{2}}}} and the related Schwartz relations, shows that the properties ...
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):
In physics, the thermal equation of state is a mathematical expression of pressure P, temperature T, and, volume V.The thermal equation of state for ideal gases is the ideal gas law, expressed as PV=nRT (where R is the gas constant and n the amount of substance), while the thermal equation of state for solids is expressed as:
The two first partial derivatives of the vdW equation are | = = | = + = where = is the isothermal compressibility (a measure of the relative increase of volume from an increase of pressure, at constant temperature), and = is the coefficient of thermal expansion (a measure of the relative increase of volume from an increase of temperature, at ...
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: ,,.
Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the pressure varies during compression: constant-temperature (isothermal ), constant-entropy (isentropic), and other variations are possible.