Compressibility

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. In its simple form, the compressibility β {displaystyle eta } may be expressed as 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. In its simple form, the compressibility β {displaystyle eta } may be expressed as where V is volume and p is pressure. The choice to define compressibility as the opposite of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume.It is also known as reciprocal of bulk modulus(k) of elasticity of a fluid. The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic 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 speed of sound is defined in classical mechanics as: where ρ {displaystyle ho } is the density of the material. It follows, by replacing partial derivatives, that the isentropic compressibility can be expressed as: The inverse of the compressibility is called the bulk modulus, often denoted K (sometimes B).The compressibility equation relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.