# What is meant by Compressibility?

Chetan Mandayam Nayakar
312 Points
12 years ago

In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.

$\beta=-\frac{1}{V}\frac{\partial V}{\partial p}$

where V is volume and p is pressure

Note: most textbooks use the notation κ for this quantity

The above statement 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:

$\beta_T=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_T$

where the subscript T indicates that the partial differential is to be taken at constant temperature

$\beta_S=-\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_S$

where S is entropy. For a solid, the distinction between the two is usually negligible.

The inverse of the compressibility is called the bulk modulus, often denoted K (sometimes B). That page also contains some examples for different materials.

The compressibility equation relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.