Tait equation of state - Revision history

Carl McBride: Slight tidy: replaced underscores with spaces.

2015-03-06T11:41:41Z

Slight tidy: replaced underscores with spaces.

← Older revision		Revision as of 13:41, 6 March 2015
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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>

Dduque: additional link to the Cole EOS

2015-03-05T10:51:36Z

additional link to the Cole EOS

← Older revision		Revision as of 12:51, 5 March 2015
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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~~, or Cole~~, EOS~~ ]]. This perhaps stems for the classic text by Cole		[[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).

Dduque: Added two more references, and a note about Cole's text

2015-03-05T10:49:42Z

Added two more references, and a note about Cole's text

← Older revision		Revision as of 12:49, 5 March 2015
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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>. 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>
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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 \| stiffened, or Cole, EOS ]]. 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 ==

Dduque: Mention to stiffened equation of state, the two are often confused

2013-10-10T11:23:28Z

Mention to stiffened equation of state, the two are often confused

← Older revision		Revision as of 13:23, 10 October 2013
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	*<math> V \ </math> is the [[specific volume]].		*<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]].

			It is quite common that this name is improperly used for the adiabatic form of the
			[[stiffened equation of state]].

	== References ==		== References ==

Carl McBride: Included page in the water category.

2012-10-18T14:33:42Z

Included page in the water category.

← Older revision		Revision as of 16:33, 18 October 2012
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	[[Category:Equations of state]]		[[Category:Equations of state]]
			[[Category: Water]]

Carl McBride: Changed notation to be consistent with SklogWiki

2012-10-18T12:46:07Z

Changed notation to be consistent with SklogWiki

← Older revision		Revision as of 14:46, 18 October 2012
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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>. 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>. 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>

	or in the integrated form		or in the integrated form

	:<math> V = V_0 - C \log \frac{B+P}{B+~~P_0~~}</math>		:<math> V = V_0 - C \log \frac{B+p}{B+p_0}</math>

	where		where

Carl McBride: Changed notation to be consistent with SklogWiki

2012-10-18T12:35:26Z

Changed notation to be consistent with SklogWiki

← Older revision		Revision as of 14:35, 18 October 2012
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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>. 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>. It may be written as

	:<math> \~~beta~~ := \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>

	or in the integrated form		or in the integrated form
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	where		where
	*<math> \~~beta~~</math> is the [[compressibility]].		*<math>\kappa_T</math> is the [[Compressibility# Isothermal compressibility \| Isothermal compressibility]]
	*<math> V \ </math> is the [[specific volume]].		*<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]].

Carl McBride: Added link to original ms

2012-10-18T12:25:47Z

Added link to original ms

← Older revision		Revision as of 14:25, 18 October 2012
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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>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>. 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>. It may be written as

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

Carl McBride: Slight tidy

2012-10-18T12:10:21Z

Slight tidy

← Older revision		Revision as of 14:10, 18 October 2012
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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 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>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>. It may be written as

	:<math> \beta := \frac{-1}{V} \left ( \frac{\partial V}{\partial P} \right )_T = \frac{1}{V} \frac{C}{B+P}</math>		:<math> \beta := \frac{-1}{V} \left ( \frac{\partial V}{\partial P} \right )_T = \frac{1}{V} \frac{C}{B+P}</math>
Line 10:		Line 10:
	*<math> \beta</math> is the [[compressibility]].		*<math> \beta</math> is the [[compressibility]].
	*<math> V \ </math> is the [[specific volume]].		*<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]].

	== References ==		== References ==
			<references/>


	[[Category:Equations of state]]		[[Category:Equations of state]]

Dduque: Improved notation, fixed typo (also in wikipedia!).

2012-10-17T20:29:49Z

Improved notation, fixed typo (also in wikipedia!).

← Older revision		Revision as of 22:29, 17 October 2012
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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.