American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: http://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
Open Access
Journal Browser
Go
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

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

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Fermi, E., Thermodynamics (Dover Books on Physics), Dover Publications, New York, 1956.
 
[2]  Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, Wiley, New York, 1985.
 
[3]  Hill, T.L., An Introduction to Statistical Thermodynamics (Dover Books on Physics), Dover Publications, New York, 1987.
 
[4]  Reynolds, W.C. and Perkins, H.C., Engineering Thermodynamics (2nd Edition), McGraw-Hill, New York, 1977.
 
[5]  Cengel, Y. and Boles, M., Thermodynamics: An Engineering Approach (8th Edition), McGraw-Hill, New York, 2014.
 
[6]  Moran, M.J., Shapiro, H.N., Boettner, D.D. and Bailey, M.B., Fundamentals of Engineering Thermodynamics (8th Edition), Wiley, New York, 2014.
 
[7]  Poisson, E., Statistical Physics I, Lecture Notes (Fall 2000), Department of Physics, University of Guelph [Online] Available: https://www.physics.uoguelph.ca/~epoisson/research/spi.pdf/ [Accessed Mar. 28, 2017].
 
[8]  Wang, C.Y. and Hou, C.H., “Teaching Differentials in Thermodynamics Using Spatial Visualization,” Journal of Chemical Education, 89 (12), 1522-1525, 2012.