Tait equation of state: Difference between revisions
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(Added two more references, and a note about Cole's text) |
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It is quite common that this name is improperly used for the adiabatic form of the | It is quite common that this name is improperly used for the adiabatic form of the | ||
[[stiffened equation of state | [[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). | <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). | ||
Revision as of 11:51, 5 March 2015
The Tait equation is an equation of state. The equation was originally published by Peter Guthrie Tait in 1888 [1][2][3]. 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 [4] calling this equation a "modified Tait equation" (p. 39).
References
- ↑ 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)
- ↑ Yuan-Hui Li "Equation of state of water and sea water", Journal of Geophysical Research 72 pp. 2665-2678 (1967)
- ↑ 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)
- ↑ Robert H Cole "Underwater explosions", Princeton University Press, Princeton (1948)