Heat capacity: Difference between revisions

Revision as of 15:17, 29 January 2008

δ Q = d U + p d V

the heat capacity is given by

C = \frac{δ Q}{\partial T}

C_{V} = {\frac{δ Q}{\partial T} |}_{V} = {\frac{\partial U}{\partial T} |}_{V}

where U is the internal energy, T is the temperature, and V is the volume.

C_{p} = {\frac{δ Q}{\partial T} |}_{p} = {\frac{\partial U}{\partial T} |}_{p} + p {\frac{\partial V}{\partial T} |}_{p}

where p is the pressure.

We have

C_{p} - C_{V} = (p + {\frac{\partial U}{\partial V} |}_{T}) {\frac{\partial V}{\partial T} |}_{p}

@@ Line 9: / Line 9: @@
 :<math>C_V = \left.\frac{\delta Q}{\partial T} \right\vert_V = \left. \frac{\partial U}{\partial T} \right\vert_V </math>
-where ''U'' is the [[internal energy]], ''T'' is the temperature, and  ''V'' is the volume.
+where ''U'' is the [[internal energy]], ''T'' is the [[temperature]], and  ''V'' is the volume.
 ==At constant pressure==
 :<math>C_p = \left.\frac{\delta Q}{\partial T} \right\vert_p = \left. \frac{\partial U}{\partial T} \right\vert_p + p \left.\frac{\partial V}{\partial T} \right\vert_p</math>