Tait equation of state

The Tait equation is an equation of state. The equation was originally published by Peter Guthrie Tait in 1888 . It may be written as

$\kappa _{T}:={\frac {-1}{V}}\left({\frac {\partial V}{\partial p}}\right)_{T}={\frac {1}{V}}{\frac {C}{B+p}}$

or in the integrated form

$V=V_{0}-C\log {\frac {B+p}{B+p_{0}}}$

where

• $\kappa _{T}$ is the Isothermal compressibility
• $V\$ is the specific volume.
• $B\$ and $C\$ are functions of temperature that are independent of pressure.

It is quite common that this name is improperly used for the adiabatic form of the stiffened equation of state , which is the Cole equation of state . This perhaps stems for the classic text by Cole calling this equation a "modified Tait equation" (p. 39).