Compressibility

The (isothermal) compressibility κT\kappa_{T} of a fluid represent how much its volume VV changes under external pressure PP at a constant temperature TT. It is defined as the coefficient

κT=−1V(∂V∂P)T=−1v(∂v∂P)T\kappa_{T}=- \frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_{T}=- \frac{1}{v}\left( \frac{ \partial v }{ \partial P } \right)_{T}

where v=V/Nv=V/N is the specific volume.