Editing SR (section)

====Components of the Total Pressure====
For ''time-dependent'' problems we usually will supplement the set of [[PGE#Principal_Governing_Equations|principal governing equations]] by adopting a relationship between the state variables {{Template:Math/VAR_Pressure01}}, {{Template:Math/VAR_Density01}}, and {{Template:Math/VAR_Temperature01}} that is given by one of the expressions in the following Table, or by [[SR/PressureCombinations#Total_Pressure|some combination of these expressions]].  (For example, we could write <math>P_\mathrm{total} = P_\mathrm{gas} + P_\mathrm{deg} + P_\mathrm{rad}</math>.)  

<table width="95%" align="center" border=1 cellpadding=5>
<tr>
<th colspan=2 align="center">
<font color="darkblue">Analytic Equations of State</font>
</th>
<td align="center" rowspan="2" width="25%"><font color="darkblue">Radiation Pressure</font></td>
</tr>
<tr>
<td align="center" width="25%"><font color="darkblue">Ideal Gas</font></td>
<td align="center"><font color="darkblue">Degenerate Electron Gas</font></td>
</tr>
<tr>
<td align="center">
{{Template:Math/EQ_EOSideal0A}}
[[Image:OtherFormsButton.jpg|150px|link=SR/IdealGas#Ideal_Gas_Equation_of_State]]
</td>
<td align="center">
{{Template:Math/EQ_ZTFG01}}
</td>
<td align="center">
{{Template:Math/EQ_EOSradiation01}}
</td>
</tr>

<tr>
<td align="center" colspan=3><font color="darkblue">Normalized Total Pressure:</font></td>
</tr>
<tr>
<tr>
<td colspan=3 align="center">
{{Template:Math/EQ_PressureTotal01}}
[[Image:OriginButton.jpg|120px|link=SR/PressureCombinations#Total_Pressure]]
</td>
</tr>

</table>

In the so-called [[SR/IdealGas#Ideal_Gas_Equation_of_State|''ideal gas'' equation of state]], {{Template:Math/C_GasConstant}} is the gas constant and {{Template:Math/MP_MeanMolecularWeight}} is the mean molecular weight of the gas. In the equation that gives the electron degeneracy pressure, {{Template:Math/C_FermiPressure}} is the characteristic Fermi pressure and {{Template:Math/C_FermiDensity}} is the characteristic Fermi density.  And in the expression for the photon radiation pressure, {{Template:Math/C_RadiationConstant}} is the radiation constant.  The value of each of these identified physical constants can be found by simply scrolling the computer mouse over the symbol for the constant found in the text of this paragraph, and a definition of each constant can be found in the [[Appendix/VariablesTemplates|Variables Appendix]] of this H_Book.

All three of these equations are among the set of [[Appendix/EquationTemplates#Equations_of_State|key physical equations]] that provide the foundation for our discussion of the '''structure, stability, and dynamics of self-gravitating fluids.'''  A discussion of the physical principles that underpin each of these relations can be found in any of a number of different published texts &#8212; see, for example, the set of ''parallel references'' identified in the [[Appendix/EquationTemplates#Equations_of_State|Equations Appendix]] of this H_Book &#8212; or in the Wiki pages that can be accessed by clicking the linked "other forms" buttons in the above Table.  See also [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] &#8212; specifically the discussion associated with his Chapter 4, Eq. 13 &#8212; for a more general statement related to the proper specification of a supplemental, equation of state relationship.