The derivation of thermodynamical relations for a simple system

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences 1935-05, Vol.234 (740), p.299-328
• Main Author: Shaw, A. Norman
• Format: Article
• Language: English
• Subjects: Cooling; Equations of state; Jacobians; Mathematical constants; Mathematical expressions; Mathematical independent variables; Partial derivatives; Second partial derivative; Specific heat; Thermodynamics
• ISSN: 0080-4614; 2054-0272
• DOI: 10.1098/rsta.1935.0009

In the majority of articles and texts requiring or explaining the applications of thermodynamics, numerous relations between partial derivatives are obtained or discussed without the adoption of a systematic method. No uniform procedure has been followed heretofore for finding quickly and easily the relation between any given derivative, and any permissible set of other derivatives chosen for reference. There is a very common practice of dealing with useful relations by the method of “presentation followed by verification,” which is most unsatisfactory. A few tables are available; in particular, the “Condensed Collection of Thermodynamical Formulas,” by P. W. Bridgman (Harvard Univ. Press) is useful and covers a large range; but in all current procedures the task of expressing a first or second partial derivative in terms of a set of others, remains in general most laborious. In the cases when the various derivatives of a chosen reference set had different pairs of independent variables, many transformations of possible interest have been neglected as altogether too complicated or too tedious for solution. If we desire to evaluate some partial derivative which cannot be obtained directly from experimental data, we should naturally choose other derivatives which have been found with the desired precision, and use them to calculate the former. Curiously, it appears that little advantage is taken of this possible procedure ; often we find that the better-known standard relations are used, when the included derivatives may not have been determined with as high a precision as some others.