Editing Tait equation of state

The '''Tait equation''' is an [[equations of state | equation of state]].  The equation was originally published by [[Peter Guthrie Tait]] in 1888 <ref>[http://archive.org/stream/reportonscientif02grea#page/n21/mode/2up P. G. Tait "Report on some of the physical properties of fresh water and sea water", Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76. Physics and chemistry '''2''' pp. 1-76 (1888)]</ref><ref>[http://dx.doi.org/10.1029/JZ072i010p02665  Yuan-Hui Li "Equation of state of water and sea water", Journal of Geophysical Research '''72''' pp. 2665-2678 (1967)]</ref><ref>[http://www.archive.org/details/supersonicflowsh00cour Richard Courant "Supersonic_flow_and_shock_waves_a_manual_on_the_mathematical_theory_of_non-linear_wave_motion", Courant Institute of Mathematical Sciences, New York University, New York (1944)]</ref>. It may be written as

:<math> \kappa_T := \frac{-1}{V} \left ( \frac{\partial V}{\partial p} \right )_T = \frac{1}{V} \frac{C}{B+p}</math>

or in the integrated form

:<math> V = V_0 - C \log \frac{B+p}{B+p_0}</math>

where
*<math>\kappa_T</math> is the [[Compressibility# Isothermal compressibility |  Isothermal compressibility]]
*<math> V \ </math> is the [[specific volume]].
*<math> B \ </math> and <math> C \ </math> 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
<ref>[http://www.archive.org/details/underwaterexplos00cole Robert H Cole "Underwater explosions", Princeton University Press, Princeton (1948)]</ref> calling this equation a "modified Tait equation" (p. 39).

== References ==
<references/>


[[Category:Equations of state]]
[[Category: Water]]
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	The '''Tait equation''' is an [[equations of state \| equation of state]]. The equation was originally published by [[Peter Guthrie Tait]] in 1888 <ref>[http://archive.org/stream/reportonscientif02grea#page/n21/mode/2up P. G. Tait "Report on some of the physical properties of fresh water and sea water", Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76. Physics and chemistry '''2''' pp. 1-76 (1888)]</ref><ref>[http://dx.doi.org/10.1029/JZ072i010p02665 Yuan-Hui Li "Equation of state of water and sea water", Journal of Geophysical Research '''72''' pp. 2665-2678 (1967)]</ref><ref>[http://www.archive.org/details/supersonicflowsh00cour Richard Courant "~~Supersonic flow and shock waves a manual on the mathematical theory of non~~-~~linear wave motion~~", Courant Institute of Mathematical Sciences, New York University, New York (1944)]</ref>. It may be written as		The '''Tait equation''' is an [[equations of state \| equation of state]]. The equation was originally published by [[Peter Guthrie Tait]] in 1888 <ref>[http://archive.org/stream/reportonscientif02grea#page/n21/mode/2up P. G. Tait "Report on some of the physical properties of fresh water and sea water", Report on the scientific results of the voyage of H.M.S. Challenger during the years 1873-76. Physics and chemistry '''2''' pp. 1-76 (1888)]</ref><ref>[http://dx.doi.org/10.1029/JZ072i010p02665 Yuan-Hui Li "Equation of state of water and sea water", Journal of Geophysical Research '''72''' pp. 2665-2678 (1967)]</ref><ref>[http://www.archive.org/details/supersonicflowsh00cour Richard Courant "Supersonic_flow_and_shock_waves_a_manual_on_the_mathematical_theory_of_non-linear_wave_motion", Courant Institute of Mathematical Sciences, New York University, New York (1944)]</ref>. It may be written as

	:<math> \kappa_T := \frac{-1}{V} \left ( \frac{\partial V}{\partial p} \right )_T = \frac{1}{V} \frac{C}{B+p}</math>		:<math> \kappa_T := \frac{-1}{V} \left ( \frac{\partial V}{\partial p} \right )_T = \frac{1}{V} \frac{C}{B+p}</math>