The Triple Product Rule is Incorrect
Igor A. Stepanov
Igor Stepanov, Scholar/Institute of Science and Innovative Technologies, Liepaja University, Liepaja, Latvia, LV-3401.
Manuscript received on 01 September 2021 | Revised Manuscript received on 06 September 2021 | Manuscript Accepted on 15 October 2021 | Manuscript published on 30 October 2021 | PP: 1-3 | Volume-1 Issue-2, October 2021 | Retrieval Number:100.1/ijam.B1102101121 | DOI: 10.54105/ijam.B1102.101221
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Abstract: The triple product rule, also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler’s chain rule, relates the partial derivatives of three interdependent variables, and often finds application in thermodynamics. It is shown here that its derivation is wrong, and that this rule is not correct; hence, the Mayer’s relation and the heat capacity ratio, which describe the difference between isobaric and isochoric heat capacities, are also untrue. Also, the relationship linking thermal expansion and isothermal compressibility is wrong. These results are confirmed by many experiments and by the previous theoretical findings of the author.
Keywords: Cyclic chain rule; Cyclic relation; Mayer’s relation; Heat capacity ratio; Isochoric heat capacity; Compressibility.
Scope of the Article: Calculus and Analysis