# Difference between revisions of "Tait equation of state"

(Mention to stiffened equation of state, the two are often confused) |
(Added two more references, and a note about Cole's text) |
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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 == |

## Revision as of 12:49, 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

or in the integrated form

where

- is the Isothermal compressibility
- is the specific volume.
- and 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, or Cole, EOS . 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)