Hostname: page-component-6766d58669-nqrmd Total loading time: 0 Render date: 2026-05-18T04:12:09.664Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermodynamics, Mnemonic Matrices and Generalized Inverses

Published online by Cambridge University Press:  17 February 2009

R. B. Leipnik  and
C. E. M. Pearce
R. B. Leipnik
Affiliation:
(Deceased October 10, 2006), Department of Mathematics, UCSB, Ca 93106-3080, USA
C. E. M. Pearce
Affiliation:
School of Mathematical Sciences, University of Adelaide, Australia 5005; email: charles.pearce@adelaide.edu.au.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We present an alternative matrix mnemonic for the basic equations of simple thermodynamics. When normalized, this permits an explicit generalized inverse, allowing inversion of the mechanical and chemical thermodynamic equations. As an application, the natural variables S, V, P and T are derived from the four energies E (internal), F (free), G (Gibbs) and H (enthalpy).

Keywords

thermodynamicsmatrix mnemonicsgeneralized inverses

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 4 , April 2007 , pp. 493 - 501
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Andrews, F. C., Thermodynamics: Principles and Applications (Wiley–Interscience, New York, 1971).Google Scholar
[2]Callen, H. B., Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985).Google Scholar
[3]Fowler, R. H., Statistical Mechanics, 2nd ed. (Cambridge University Press, Cambridge-New York, 1936).Google Scholar
[4]Fox, R. F., “The thermodynamic cuboctahedron model”, J. Chem. Educ. 53 (1976) 441–442.Google Scholar
[5]Gilmore, R., “Thermodynamic partial derivatives by matrices”, J Chem. Phys. 75 (1981) 5964–5966.CrossRefGoogle Scholar
[6]Koenig, F. O., “Families of thermodynamic equations I”, J. Chem. Phys. 3 (1935) 29–35.CrossRefGoogle Scholar
[7]Lee, K. C., “How to teach statistical thermal physics”, Amer. J. Phys. 69 (2001) 68–75.CrossRefGoogle Scholar
[8]Moore, E. H., “General analysis, part I”, Memoirs Amer. Phil. Soc. 1 (1935) 1–231.Google Scholar
[9]Pate, S. F., “The thermodynamic cube”, Amer. J. Phys. 67 (1999) 1111–1113.CrossRefGoogle Scholar
[10]Penrose, R. M., “A generalized inverse for matrices”, Proc. Camb. Phil. Soc. 51 (1955) 406–413.CrossRefGoogle Scholar
[11]Strang, G., Linear Algebra and its Applications, 3rd ed. (Harcourt, Brace, Jovanovich, New York, 1988).Google Scholar
[12]Weinhold, F., “Metric geometry of equilibrium thermodynamics I, II, III, IV”, J. Chem. Phys. 63 (1975) 2479–2501.CrossRefGoogle Scholar