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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V = V_0 - C \log \frac{B+p}{B+p_0}}

where

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa_T} is the Isothermal compressibility
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V \ } is the specific volume.
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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, or Cole, EOS . This perhaps stems for the classic text by Cole calling this equation a "modified Tait equation" (p. 39).