The Internal Energy of a PV = RT Gas: A Univariable or Multivariable Function

Authors: Stracher G.B.¹; Guy A.G.²

Source: Mathematical Geology, Volume 30, Number 3, April 1998 , pp. 251-258(8)

Publisher: Springer

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Abstract:

Historically, the characterization of the internal energy of a simple gas is based on free expansion experiments and imprecise use of the word function, which is rigorously defined in mathematics. Univariable equations of state show that the internal energy of simple monatomic, diatomic, and polyatomic gases can be expressed as a “function” of temperature “only”. However, multivariable equations of state derived from composite functions confirm that the internal energy of these gases can in each situation also be expressed as a “function” of pressure and volume “only”. It is essential that the mathematical definition of the word function be adhered to in science because it is fundamental for the formulation of the calculus, a mathematical tool essential for solving a variety of thermodynamics problems.

Keywords: first law; free expansion; heat capacity; equations of state

Language: English

Document Type: Research article

Affiliations: 1: Department of Geology, East Georgia College, University System of Georgia, Swainsboro, Georgia 30401. stracher@mail.ega.peachnet.edu 2: Materials Science and Engineering, University of Florida, Gainesville, Florida. Mailing address: 3939 NE 5th Avenue, Apt. E105, Boca Raton, Florida 33431

Publication date: 1998-04-01