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Ideal Gas Relations
Much of the following overview of ideal gas relations is drawn from Chapter II of Chandrasekhar's classic text on Stellar Structure [C67], which was originally published in 1939. A guide to parallel discussions of this topic is provided alongside the ideal gas equation of state in the key equations appendix of this H_Book.
Property #1
An ideal gas containing <math>~n_g</math> free particles per unit volume will exert on its surroundings an isotropic pressure (i.e., a force per unity area) <math>~P</math> given by the following
Standard Form
of the Ideal Gas Equation of State,
<math>~P = n_g k T</math>
if the gas is in thermal equilibrium at a temperature <math>~T</math>.
Property #2
The internal energy per unit mass <math>~\epsilon</math> of an ideal gas is a function only of the gas temperature <math>~T</math>, that is,
<math> \epsilon = \epsilon(T) </math>.
Conservative Form
of the Continuity Equation,
<math>~P = (\gamma_\mathrm{g} - 1)\epsilon \rho </math>
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