Thermodynamic relations: Difference between revisions

Latest revision as of 15:10, 5 October 2011

Notation used:

These thermodynamic relations are also known as coefficient relations.

$T=\left({\frac {\partial U}{\partial S}}\right)_{V}$

$p=-\left({\frac {\partial U}{\partial V}}\right)_{S}$

$T=\left({\frac {\partial H}{\partial S}}\right)_{p}$

$V=\left({\frac {\partial H}{\partial p}}\right)_{S}$

$S=-\left({\frac {\partial A}{\partial T}}\right)_{V}$

$p=-\left({\frac {\partial A}{\partial V}}\right)_{T}$

$S=-\left({\frac {\partial G}{\partial T}}\right)_{p}$

$V=\left({\frac {\partial G}{\partial p}}\right)_{T}$

@@ Line 1: / Line 1: @@
- Also known as coefficient relations.
+<div style="border:1px solid #f3f3ff; padding-left: 0.5em !important; background-color: #f3f3ff; border-width: 0 0 0 1.4em; clear:right; float:right;">
+Notation used:
+*<math>H</math> is the [[enthalpy]]
+*<math>T</math> is the [[temperature]]
+*<math>G</math> is the [[Gibbs energy function]]
+*<math>U</math> is the [[internal energy]],
+*<math>V</math> is the volume
+*<math>A</math> is the [[Helmholtz energy function]]
+*<math>p</math> is the [[pressure]]
+*<math>S</math> is the [[entropy]]
+</div>
+These '''thermodynamic relations''' are also known as ''coefficient relations''.
 <math>T=\left(\frac{\partial U}{\partial S}\right)_V </math>
-<math> P=-\left(\frac{\partial U}{\partial V}\right)_S </math>
+<math> p=-\left(\frac{\partial U}{\partial V}\right)_S </math>
 <math>T=\left(\frac{\partial H}{\partial S}\right)_p </math>
@@ Line 9: / Line 20: @@
 <math> V=\left(\frac{\partial H}{\partial p}\right)_S </math>
-<math>S=-\left(\frac{\partial F}{\partial T}\right)_V </math>
+<math>S=-\left(\frac{\partial A}{\partial T}\right)_V </math>
 <math> p=-\left(\frac{\partial A}{\partial V}\right)_T </math>
@@ Line 17: / Line 28: @@
 <math> V=\left(\frac{\partial G}{\partial p}\right)_T </math>
+==See also==
+*[[Maxwell's relations]]
+*[[Bridgman thermodynamic formulas]]
+[[Category: Classical thermodynamics]]