Editing Equation of state (section)

=== Stiffened equation of state ===

When considering water under very high pressures, in situations such as [[Underwater explosion|underwater nuclear explosions]], [[Extracorporeal shock wave lithotripsy|sonic shock lithotripsy]], and [[sonoluminescence]], the stiffened equation of state<ref>{{Cite journal|last1=Le Métayer|first1=O|last2=Massoni|first2=J|last3=Saurel|first3=R|date=2004-03-01|title=Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques|url=https://www.sciencedirect.com/science/article/pii/S1290072903001443|journal=International Journal of Thermal Sciences|language=fr|volume=43|issue=3| pages=265–276| doi=10.1016/j.ijthermalsci.2003.09.002|issn=1290-0729}}</ref> is often used:

<math display="block">p = \rho(\gamma - 1)e - \gamma p^0 \,</math>

where <math>e</math> is the internal energy per unit mass, <math>\gamma</math> is an empirically determined constant typically taken to be about 6.1, and <math>p^0</math> is another constant, representing the molecular attraction between water molecules. The magnitude of the correction is about 2 gigapascals (20,000 atmospheres).

The equation is stated in this form because the speed of sound in water is given by <math>c^2 = \gamma\left(p + p^0\right)/\rho</math>.

Thus water behaves as though it is an ideal gas that is ''already'' under about 20,000 atmospheres (2&nbsp;GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100&nbsp;kPa to 200&nbsp;kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 atmospheres (2000.1&nbsp;MPa to 2000.2&nbsp;MPa).

This equation mispredicts the [[specific heat capacity]] of water but few simple alternatives are available for severely nonisentropic processes such as strong shocks.