Open AccessThe Triple Product Rule is Incorrect
Author(s) -
I. A. Stepanov,
AUTHOR_ID
Publication year - 2021
Publication title -
indian journal of advanced mathematics
Language(s) - English
Resource type - Journals
ISSN - 2582-8932
DOI - 10.54105/ijam.b1102.101221
Subject(s) - isobaric process , isochoric process , sum rule in quantum mechanics , thermodynamics , compressibility , product (mathematics) , chain rule (probability) , isothermal process , relation (database) , heat capacity , mathematics , statistical physics , computer science , physics , econometrics , data mining , volatility (finance) , conditional variance , geometry , quantum mechanics , quantum chromodynamics , autoregressive conditional heteroskedasticity
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.