American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: Editor-in-chief: Ratko Pavlović
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American Journal of Educational Research. 2017, 5(4), 362-366
DOI: 10.12691/education-5-4-4
Open AccessArticle

Educational Efficacy of Derivation Method for Partial Differential Equations in Thermodynamics

Tetsuya Kanagawa1, 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

Pub. Date: April 12, 2017

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


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.

thermodynamics partial derivative total differential physics education

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