Tait equation of state: Difference between revisions

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The '''Tait equation''' is an [[equation of state]].  The equation was originally published by Peter Guthrie Tait in 1888. (Yuan-Hui Li, 15 May 1967, Equation of State of Water and Sea Water, Journal of Geophysical Research 72 (10), p. 2665.)  It is sometimes written as
The '''Tait equation''' is an [[equation of state]].  The equation was originally published by Peter Guthrie Tait in 1888. (Yuan-Hui Li, 15 May 1967, Equation of State of Water and Sea Water, Journal of Geophysical Research 72 (10), p. 2665.)  It may be written as


:<math> \beta_0^{(P)} = \frac{-1}{V_0^{(P)}} \left ( \frac{\partial V}{\partial P} \right )_T = \frac{0.4343C}{V_0^{(P)}(B+P)}</math>
:<math> \beta := \frac{-1}{V} \left ( \frac{\partial V}{\partial P} \right )_T = \frac{1}{V} \frac{C}{B+P}</math>


or in the integrated form
or in the integrated form


:<math> V_0^{(P)} = V_0^{(1)} - C \log \frac{B+P}{B+1}</math>
:<math> V = V_0 - C \log \frac{B+P}{B+P_0}</math>


where
where
*<math> \beta_0^{(P)} </math> is the compressibility of water.
*<math> \beta</math> is the [[compressibility]].
*<math> V_0 \ </math> is the specific volume of water
*<math> V \ </math> is the [[specific volume]].
*<math> B \ </math> and <math> C \ </math> are functions of temperature that are independent of pressure.
*<math> B \ </math> and <math> C \ </math> are functions of temperature that are independent of pressure.



Revision as of 21:29, 17 October 2012

The Tait equation is an equation of state. The equation was originally published by Peter Guthrie Tait in 1888. (Yuan-Hui Li, 15 May 1967, Equation of State of Water and Sea Water, Journal of Geophysical Research 72 (10), p. 2665.) It may be written as

or in the integrated form

where

  • is the compressibility.
  • is the specific volume.
  • and are functions of temperature that are independent of pressure.

References