%0 Journal Article %1 einbinder1953application %A Einbinder, Harvey %D 1953 %J The Journal of Chemical Physics %K 1953 Jacobian properties thermodynamic %N 12 %P 2134-2142 %R 10.1063/1.1698800 %T The Application of Jacobians to Statistical Thermodynamics %U http://dx.doi.org/10.1063/1.1698800 %V 21 %X Shaw's Jacobian method for calculating thermodynamic derivatives is extended so that any partial second derivative can be expressed in terms of two sets of reference derivatives based on the independent variables (V, T) and (P, T), respectively. A simplified and enlarged table of second‐order Jacobians is given in terms of these reference sets. Methods are developed for obtaining the reference J's explicitly in the cases of greatest importance in statistical thermodynamics, i.e., from A, E, the partition function and the caloric equation PV=sE, permitting any first or second partial derivative to be found as an explicit function of (V, T). These J's are given for the polyatomic ideal and van der Waals gases, black‐body radiation, the general (relativistic and nonrelativistic) quantum gas, and the general degenerate Bose‐Einstein and Fermi‐Dirac gases. Their great usefulness is illustrated, and the possible application of reference Jacobians in evaluating semi‐empirical theories of liquids and gases is noted. Finally, the classical theory of thermodynamic fluctuations is extended using Jacobians. General formulas are derived which give explicitly the total variance, partial variance, and covariance of the fluctuation of any thermodynamic variable from its equilibrium value.

@article{einbinder1953application, abstract = {Shaw's Jacobian method for calculating thermodynamic derivatives is extended so that any partial second derivative can be expressed in terms of two sets of reference derivatives based on the independent variables (V, T) and (P, T), respectively. A simplified and enlarged table of second‐order Jacobians is given in terms of these reference sets. Methods are developed for obtaining the reference J's explicitly in the cases of greatest importance in statistical thermodynamics, i.e., from A, E, the partition function and the caloric equation PV=sE, permitting any first or second partial derivative to be found as an explicit function of (V, T). These J's are given for the polyatomic ideal and van der Waals gases, black‐body radiation, the general (relativistic and nonrelativistic) quantum gas, and the general degenerate Bose‐Einstein and Fermi‐Dirac gases. Their great usefulness is illustrated, and the possible application of reference Jacobians in evaluating semi‐empirical theories of liquids and gases is noted. Finally, the classical theory of thermodynamic fluctuations is extended using Jacobians. General formulas are derived which give explicitly the total variance, partial variance, and covariance of the fluctuation of any thermodynamic variable from its equilibrium value.}, added-at = {2015-02-17T13:58:06.000+0100}, author = {Einbinder, Harvey}, biburl = {https://www.bibsonomy.org/bibtex/208ddcee28d74bd270b8823df67610817/thorade}, description = {The Application of Jacobians to Statistical Thermodynamics}, doi = {10.1063/1.1698800}, eid = {2134}, interhash = {3b9e7839a2bbd7f1c96fbd848ec885a6}, intrahash = {08ddcee28d74bd270b8823df67610817}, journal = {The Journal of Chemical Physics}, keywords = {1953 Jacobian properties thermodynamic}, number = 12, pages = {2134-2142}, timestamp = {2015-02-17T13:58:06.000+0100}, title = {The Application of Jacobians to Statistical Thermodynamics}, url = {http://dx.doi.org/10.1063/1.1698800}, volume = 21, year = 1953 }