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==Equations of State==

===<span id="EOS:IdealGas">Ideal Gas</span>===
The ideal gas equation of state is referred to as the [http://en.wikipedia.org/wiki/Ideal_gas_law ideal gas law] in Wikipedia.  The Wikipedia discussion points out that, as derived from first principles in statistical mechanics, this "gas law" can most naturally be written in the form,
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<math>P = \biggl( \frac{N}{V} \biggr) kT</math>
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where {{User:Tohline/Math/VAR_Pressure01}}, {{User:Tohline/Math/VAR_Temperature01}} and {{User:Tohline/Math/C_BoltzmannConstant}} are as we have defined them in our accompanying [http://www.vistrails.org/index.php/User:Tohline/Appendix/Variables_templates variables appendix], and the ratio <math>(N/V)</math> specifies the number density of free particles that make up the gas.  The number density of free particles also can be written as a ratio of the mass density, {{User:Tohline/Math/VAR_Density01}}, to the average mass per free particle, <math>\bar{m}</math>, that is, the ideal gas equation of state may be written in the form,
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<math>P = \biggl( \frac{\rho}{\bar{m}} \biggr) kT</math> .
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It is customary in astrophysical discussions to write the average mass per free particle as {{User:Tohline/Math/MP_MeanMolecularWeight}}<math>m_u</math>, that is, as a product of the atomic mass unit, <math>m_u</math> = 1/{{User:Tohline/Math/C_AvogadroConstant}}, and a dimensionless coefficient of order unity referred to as the the mean molecular weight, {{User:Tohline/Math/MP_MeanMolecularWeight}}.  This leads to what we will refer to as, 

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<font color="red">Form A</font><br />
of the ideal gas equation of state<br />

{{User:Tohline/Math/EQ_EOSideal0A}} .
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