Compressible
In thermodynamics and fluid mechanics, compressibility (also known as the coefficient of compressibility or isothermal compressibility) is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
where V is volume and p is pressure.
The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal. Accordingly, isothermal compressibility is defined:
where the subscript T indicates that the partial differential is to be taken at constant temperature.
Isentropic compressibility is defined:
where S is entropy. For a solid, the distinction between the two is usually negligible.
The minus sign makes the compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume.
The speed of sound is defined in classical mechanics as:
where is the density of the material. It follows, by replacing partial derivatives, that the isentropic compressibility can be expressed as:
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