Educational Efficacy of Derivation Method for Partial Differential Equations in Thermodynamics

Tetsuya Kanagawa^1, and Hisao Taira²

¹Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba 305-8573, Japan

²Department of Education, Hokkaido University of Education, Sapporo Campus, Sapporo 002-8502, Japan

Cite this paper:
Tetsuya Kanagawa and Hisao Taira. Educational Efficacy of Derivation Method for Partial Differential Equations in Thermodynamics. American Journal of Educational Research. 2017; 5(4):362-366. doi: 10.12691/education-5-4-4

Abstract

One of the mathematical difficulties with regard to thermodynamics for undergraduate university students is the treatment of the total differential, which contains partial derivatives. The conventional treatment suppresses the derivation of the partial differential equations (e.g., energy equation and Mayer’s relation), reducing the student’s understanding of the physical aspects of thermodynamics. This paper proposes a systematic method for of deriving the partial differential equations in thermodynamics, based on both the total differential and the appropriate selection of independent variables of the thermodynamic state variables. To demonstrate our method, the energy equation and Mayer’s relation are derived via the systematic approach, and students’ misunderstandings concerning the derivation process are presented. The results of a questionnaire administered to evaluate student opinions indicate that our proposed method is effective.

Keywords:
thermodynamics partial derivative total differential physics education

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