Bridgman thermodynamic formulas: Difference between revisions

Revision as of 10:47, 6 October 2011

Notation used (from Table I):

Bridgman thermodynamic formulas ^[1]

{\partial T |}_{p} = - {\partial p |}_{T} = 1

{\partial V |}_{p} = - {\partial p |}_{V} = {\frac{\partial V}{\partial T} |}_{p}

{\partial S |}_{p} = - {\partial p |}_{S} = C_{p} / T

{\partial Q |}_{p} = - {\partial p |}_{Q} = C_{p}

{\partial W |}_{p} = - {\partial p |}_{W} = p {\frac{\partial V}{\partial T} |}_{p}

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

{\partial H |}_{p} = - {\partial p |}_{H} = C_{p}

{\partial G |}_{p} = - {\partial p |}_{G} = - S

{\partial A |}_{p} = - {\partial p |}_{A} = - (S + p {\frac{\partial V}{\partial T} |}_{p})

{\partial V |}_{T} = - {\partial T |}_{V} = - {\frac{\partial V}{\partial p} |}_{T}

{\partial S |}_{T} = - {\partial T |}_{S} = {\frac{\partial V}{\partial T} |}_{p}

{\partial Q |}_{T} = - {\partial T |}_{Q} = T {\frac{\partial V}{\partial T} |}_{p}

{\partial W |}_{T} = - {\partial T |}_{W} = - p {\frac{\partial V}{\partial p} |}_{T}

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

{\partial H |}_{T} = - {\partial T |}_{H} = - V + T {\frac{\partial V}{\partial T} |}_{p}

{\partial G |}_{T} = - {\partial T |}_{G} = - V

{\partial A |}_{T} = - {\partial T |}_{A} = p {\frac{\partial V}{\partial p} |}_{T}

{\partial S |}_{V} = - {\partial V |}_{S} = 1 / T (C_{p} {\frac{\partial V}{\partial p} |}_{T} + T {{(\frac{\partial V}{\partial T})}^{2} |}_{p})

{\partial Q |}_{V} = - {\partial V |}_{Q} = C_{p} {\frac{\partial V}{\partial p} |}_{T} + T {{(\frac{\partial V}{\partial T})}^{2} |}_{p}

{\partial W |}_{V} = - {\partial V |}_{W} = 0

{\partial U |}_{V} = - {\partial V |}_{U} = C_{p} {\frac{\partial V}{\partial p} |}_{T} + T {{(\frac{\partial V}{\partial T})}^{2} |}_{p}

{\partial H |}_{V} = - {\partial V |}_{H} = C_{p} {\frac{\partial V}{\partial p} |}_{T} + T {{(\frac{\partial V}{\partial T})}^{2} |}_{p} - V {\frac{\partial V}{\partial T} |}_{p}

{\partial G |}_{V} = - {\partial V |}_{G} = - (V {\frac{\partial V}{\partial T} |}_{p} + S {\frac{\partial V}{\partial p} |}_{T})

{\partial A |}_{V} = - {\partial V |}_{A} = - S {\frac{\partial V}{\partial p} |}_{T}

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 ====volume====
+:<math> \left. \partial S \right\vert_V  =  - \left. \partial V \right\vert_S = 1/T  \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T +  T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p   \right)</math>
+:<math> \left. \partial Q \right\vert_V  =  - \left. \partial V \right\vert_Q =  C_p\left. \frac{\partial V}{\partial p} \right\vert_T +  T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p  </math>
+:<math> \left. \partial W \right\vert_V  =  - \left. \partial V \right\vert_W = 0 </math>
+:<math> \left. \partial U \right\vert_V  =  - \left. \partial V \right\vert_U =  C_p\left. \frac{\partial V}{\partial p} \right\vert_T +  T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p  </math>
+:<math> \left. \partial H \right\vert_V  =  - \left. \partial V \right\vert_H =  C_p\left. \frac{\partial V}{\partial p} \right\vert_T +  T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p   - V\left.  \frac{\partial V}{\partial T} \right\vert_p </math>
+:<math> \left. \partial G \right\vert_V  =  - \left. \partial V \right\vert_G =  - \left(  V \left. \frac{\partial V}{\partial T} \right\vert_p + S\left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>
+:<math> \left. \partial A \right\vert_V  =  - \left. \partial V \right\vert_A =  -S\left. \frac{\partial V}{\partial p} \right\vert_T  </math>
+====entropy====
 ==See also==