Compressibility

The bulk modulus B gives the change in volume of a solid substance as the pressure on it is changed,

$B=-V\frac{\partial p}{\partial V}$

The compressibility K or $\kappa$, is given by

$\kappa =\frac{1}{B}$

Isothermal compressibility

The isothermal compressibility, ${\kappa }_T$ is given by

${\kappa }_T=-\frac{1}{V}{\frac{\partial V}{\partial p}|}_T=\frac{1}{\rho }{\frac{\partial \rho }{\partial p}|}_T$

(Note: in Hansen and McDonald the isothermal compressibility is written as ${\chi }_T$). where $T$ is the temperature, $\rho$ is the particle number density given by

$\rho =\frac{N}{V}$

where $N$ is the total number of particles in the system, i.e.

$N={\int }_V\rho (\mathbf{r},t)\mathrm{d}\mathbf{r}$

Adiabatic compressibility

The adiabatic compressibility, ${\kappa }_S$ is given by

${\kappa }_S=-\frac{1}{V}{\frac{\partial V}{\partial p}|}_S$

where $S$ is the entropy.

See also

The compressibility equation in statistical mechanics.