Difference between revisions of "Tait equation of state"

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(Version 1.0 ripped from wikipedia, work in progress...)
 
(Improved notation, fixed typo (also in wikipedia!).)
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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.
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*<math> \beta</math> is the [[compressibility]].
*<math> V_0 \ </math> is the specific volume of water
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*<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 22:29, 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

 \beta := \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

References