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Cengel, Y. and Boles, M., Thermodynamics: An Engineering Approach (8th Edition), McGraw-Hill, New York, 2014.

has been cited by the following article:

Article

Educational Efficacy of Derivation Method for Partial Differential Equations in Thermodynamics

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


American Journal of Educational Research. 2017, Vol. 5 No. 4, 362-366
DOI: 10.12691/education-5-4-4
Copyright © 2017 Science and Education Publishing

Cite this paper:
Tetsuya Kanagawa, 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.

Correspondence to: Tetsuya  Kanagawa, Department of Engineering Mechanics and Energy, University of Tsukuba, Tsukuba 305-8573, Japan. Email: kanagawa@kz.tsukuba.ac.jp

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.

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