Tait equation of state: Difference between revisions

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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.
*<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

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 \beta := \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 \beta} is the 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.

References