The Internal Energy of a PV = RT Gas: A Univariable or Multivariable Function1

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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.

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