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== Clausius&ndash;Clapeyron equation ==

<div class="definition"><div class="short_definition">(''Also called'' Clapeyron equation, Clapeyron&ndash;Clausius equation.) The  differential equation relating [[pressure]] of a substance to [[temperature]] in a system in which two  phases of the substance are in [[equilibrium]].</div><br/> <div class="paragraph">Two general expressions are  <div class="display-formula"><blockquote>[[File:ams2001glos-Ce17.gif|link=|center|ams2001glos-Ce17]]</blockquote></div> where ''p'' is the pressure, ''T'' the temperature, &delta;''s'' the difference in [[specific entropy]] between the  phases, &delta;''v'' the difference in [[specific volume]] between the two phases, and ''L'' the [[latent heat]] of  the [[phase change]]. The form most familiar in meteorology, related to the phase change between  [[water vapor]] and liquid water, is obtained after some approximations as  <div class="display-formula"><blockquote>[[File:ams2001glos-Ce18.gif|link=|center|ams2001glos-Ce18]]</blockquote></div> where ''e''<sub>''s''</sub> is the [[saturation vapor pressure]] of water, ''L''<sub>''v''</sub> the latent heat of [[vaporization]], and ''R''<sub>''v''</sub>  the [[gas constant]] for water vapor. A similar relation for the saturation vapor pressure in contact  with an [[ice]] surface is obtained by replacing the latent heat of vaporization by that of [[sublimation]].  These equations may be integrated to obtain explicit relationships between ''e''<sub>''s''</sub> and ''T'', given known  values at some point. The most empirically accurate relationships differ slightly from results so  obtained. An expression believed accurate to 0.3% for -35&#x000b0;C &lt; ''T'' &lt; 35&#x000b0;C is given by Bolton as   <div class="display-formula"><blockquote>[[File:ams2001glos-Ce19.gif|link=|center|ams2001glos-Ce19]]</blockquote></div>  where ''T'' is temperature in &#x000b0;C and [[vapor pressure]] is in kPa.</div><br/> </div><div class="reference">Iribarne, J. V., and W. L. Godson. 1981. ''Atmospheric Thermodynamics''. D. Reidel, p. 65. </div><br/> <div class="reference">Bolton, D. 1980. The computation of equivalent potential temperature. ''Mon. Wea. Rev.'', '''108'''. 1046&ndash;1053. </div><br/> 

<p>''Term edited 1 June 2022.''</p>

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