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

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 := \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 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 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).