A measure of resistance of a Continuum body to compression.

It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the density $\begin{array}{l}\rho\end{array}$ or molar volume $\begin{array}{l}V_m\end{array}$ :

(1)	$\begin{array}{l}\displaystyle K = \rho \cdot \frac{\partial p}{\partial \rho} = - V_m \cdot \frac{\partial p}{\partial V_m}\end{array}$

It is inverse to compressibility $\begin{array}{l}c\end{array}$ :

(2)	$\begin{array}{l}\displaystyle K = \frac{1}{c}\end{array}$

Bulk modulus depends on the thermodynamic conditions at which it is measured and as such is not a material property.

The most popular material Bulk modulus are:

Isothermal Bulk modulus

Isentropic Bulk modulus

$\begin{array}{l}T = \rm const\end{array}$

$\begin{array}{l}S = \rm const\end{array}$

(3)	$\begin{array}{l}\displaystyle K_T = \rho \left( \frac{\partial p}{\partial \rho} \right)_T\end{array}$

(4)	$\begin{array}{l}\displaystyle K_S = \rho \left( \frac{\partial p}{\partial \rho} \right)_S\end{array}$

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See also