Editing PGE/FirstLawOfThermodynamics (section)

===Example B===
In addition to the pair of source/sink terms that arise from the ''general equation of heat transfer'', [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] includes another pair of terms that often arise in discussions of stellar structure and evolution.  Specifically, on p. 56, his equation (65) states,
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\rho T \frac{ds_\mathrm{tot}}{dt} = \rho T \frac{d}{dt}\biggl( s_\mathrm{fluid} + s_\mathrm{rad} \biggr)</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>
\Psi - \nabla\cdot \vec{F}_\mathrm{cond} + \rho \epsilon_\mathrm{nuc} - \nabla \cdot \vec{F}_\mathrm{rad} \, .
</math>
  </td>
</tr>
</table>
[<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>], &sect;3.4, p. 56, Eq. (65)<br />
[<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>], Vol. II, &sect;4, p. 53, Eq. (4.40)
</div>
(Note, that [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] uses the variable notation <math>~\Phi_v</math> in place of <span title="Rate of viscous dissipation"><math>\Psi</math></span>.)  
In this expression, <math>\epsilon_\mathrm{nuc}(\rho,T)</math> expresses the rate at which (specific) energy is released via thermonuclear reactions, and
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\vec{F}_\mathrm{rad}</math>
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>- \frac{c}{3\rho\kappa_R} \nabla (a_\mathrm{rad}T^4) </math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>-\chi_\mathrm{rad} \nabla T \, ,</math>
  </td>
</tr>
<tr>
  <td align="center" colspan="3">
[<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>], Vol. I, &sect;2, p. 17, Eq. (2.17)
  </td>
  <td align="left" colspan="2">and &nbsp; &nbsp;[<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>], &sect;3.4, p. 57, Eq. (67)
  </td>
</tr>
</table>
</div>
where [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] refers to 
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>\chi_\mathrm{rad}</math>
  </td>
  <td align="center">
<math>\equiv</math>
  </td>
  <td align="left">
<math>
\frac{4c a_\mathrm{rad} T^3}{3\kappa \rho} \, ,
</math>
  </td>
</tr>
</table>
[<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>], &sect;3.4, p. 57, Eq. (68)
</div>
as the coefficient of ''radiative'' conductivity.  The expression for the radiation flux, <math>\vec{F}_\mathrm{rad}</math>, presented by [<b>[[Appendix/References#T78|<font color="red">T78</font>]]</b>] is identical ''in form'' to the expression presented above for the flux due to heat conduction, <math>\vec{F}_\mathrm{cond}</math>.  This highlights the similarities between the manner in which nature handles transport processes ("[https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law Fourier's law]") &#8212; whether by heat conduction (electrons) or radiative diffusion (photons).  


<table border="1" cellpadding="15" align="center" width="80%"><tr><td align="left">
Alternatively,<sup>&dagger;</sup> "<font color="#007700">&hellip; recognizing <math>aT^4</math> as the energy density of blackbody radiation, we see that</font> [the expression for <math>\vec{F}_\mathrm{rad}</math> that appears as equation (2.17) in Volume I of <b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>] <font color="#007700">has the general form for diffusive fluxes ([https://en.wikipedia.org/wiki/Fick's_laws_of_diffusion#Fick's_first_law Fick's law]):</font> 
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
diffusive flux
  </td>
  <td align="center">
<math>=</math>
  </td>
  <td align="left">
<math>- \mathcal{D} \nabla</math>(density of quantity being diffused),
  </td>
</tr>
</table>
<font color="#007700">where <math>\mathcal{D}</math> is the diffusivity.  Indeed, this comparison allows us to identify the radiative diffusivity as having the characteristic formula,</font>
<div align="center">
<math>~\mathcal{D}_\mathrm{rad} = \frac{1}{3} c \ell \, ,</math>
</div>
<font color="#007700">where <math>~\ell \equiv 1/\rho\kappa_R</math> is the (Rosseland) mean-free path of the diffusing particles (photons).  A 'random walk' slows down the free-flight speed {{ Template:Math/C_SpeedOfLight }} by a typical factor of <math>\ell/R_\odot</math>, so that the time <math>R_\odot^2/\mathcal{D}_\mathrm{rad}</math> for photons to diffuse to the surface of the Sun is roughly <math>3R_\odot/\ell</math> times longer than the free-flight time <math>R_\odot/c</math> of 2 s.  This process prevents the Sun from releasing its considerable internal reservoir of photons in one powerful blast, but instead regulates it to the stately observed luminosity of <math>L_\odot = 3.86 \times 10^{33}</math> erg s<sup>-1</sup>.</font>"
</td></tr>
<tr><td align="left"><sup>&dagger;</sup>Text in a green font has been taken directly from Volume I, &sect;2, p. 17 of [<b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]]</b>].
</td></tr></table>