Appendix/VariablesTemplates - Revision history

Xxsrm: Created page with "=Variables Templates= ==Physical Constants==

To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...
{{ Math/Template_Name }}

Symbol <..."
2023-12-12T19:09:34Z

Created page with "=Variables Templates= ==Physical Constants== <div align="center"> <table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue"> <tr> <td colspan=4> To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center> {{ Math/<i><font color="red">Template_Name</font></i> }}</center> </td> </tr> <tr> <th width="8%"> <font color="red">Symbol</font> </th> <th> <..."

New page
=Variables Templates=

==Physical Constants==

<div align="center">
<table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue">
<tr>
<td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
{{ Math/<i><font color="red">Template_Name</font></i> }}</center>
</td>
</tr>
<tr>
<th width="8%">
<font color="red">Symbol</font>
</th>
<th>
<font color="red">Definition</font>
</th>
<th width="25%">
<font color="red">Template_Name</font>
</th>
<th width="10%">
<font color="red">Unicode</font>
</th>
</tr>

<tr>
<td align="center">
{{ Math/C_SpeedOfLight}}
</td>
<td>
<font color="green">Speed of light</font>;   
[http://en.wikipedia.org/wiki/Speed_of_light Authoritative Value]
</td>
<td>
[[Template:Math/C_SpeedOfLight|C_SpeedOfLight]]
</td>
<td align="center">
x0063
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_GravitationalConstant}}
</td>
<td>
<font color="green">Newtonian gravitational constant</font>;   
[http://en.wikipedia.org/wiki/Gravitational_constant Authoritative Value]
</td>
<td>
[[Template:Math/C_GravitationalConstant|C_GravitationalConstant]]
</td>
<td align="center">
x0047
</td>
</tr>

<tr>
<td align="center">
{{ Math/C PlanckConstant}}
</td>
<td>
<font color="green">Planck constant</font>;   
[http://en.wikipedia.org/wiki/Planck_constant Authoritative Value];   
NOTE: <span title="h-bar"><math>\hbar</math></span> <math>\equiv</math> {{ Math/C_PlanckConstant }}/(2<math>\pi</math>)
</td>
<td>
[[Template:Math/C_PlanckConstant|C_PlanckConstant]]
</td>
<td align="center">
x0068
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_BoltzmannConstant}}
</td>
<td>
<font color="green">Boltzmann constant</font>;   
[http://en.wikipedia.org/wiki/Boltzmann_constant Authoritative Value]
</td>
<td>
[[Template:Math/C_BoltzmannConstant|C_BoltzmannConstant]]
</td>
<td align="center">
x006B
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_AvogadroConstant}}
</td>
<td>
<font color="green">Avogadro constant</font>;   
[http://en.wikipedia.org/wiki/Avogadro_constant Authoritative Value]
</td>
<td>
[[Template:Math/C_AvogadroConstant|C_AvogadroConstant]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_ElectronMass}}
</td>
<td>
<font color="green">Electron mass</font>;   
[http://en.wikipedia.org/wiki/Electron_mass Authoritative Value]
</td>
<td>
[[Template:Math/C_ElectronMass|C_ElectronMass]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_ProtonMass}}
</td>
<td>
<font color="green">Proton mass</font>;   
[http://en.wikipedia.org/wiki/Proton_mass Authoritative Value]
</td>
<td>
[[Template:Math/C_ProtonMass|C_ProtonMass]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_AtomicMassUnit}}
</td>
<td>
<font color="green">Atomic mass unit</font>;   
[http://en.wikipedia.org/wiki/Atomic_mass_unit Authoritative Value];   
NOTE: {{ Math/C_ProtonMass }}/{{ Math/C_AtomicMassUnit }} = 1.007276
</td>
<td>
[[Template:Math/C_AtomicMassUnit|C_AtomicMassUnit]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_GasConstant}}
</td>
<td>
<font color="green">Gas constant</font> = {{ Math/C_BoltzmannConstant }}{{ Math/C_AvogadroConstant }} = 1.007276 {{ Math/C_BoltzmannConstant }}/{{ Math/C_ProtonMass }};   
[http://en.wikipedia.org/wiki/Gas_constant Authoritative Value]

</td>
<td>
[[Template:Math/C_GasConstant|C_GasConstant]]
</td>
<td align="center">
x211C
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_FermiPressure}}
</td>
<td>
<font color="green">Characteristic Fermi pressure</font>; <br />
<math>A_\mathrm{F} \equiv \frac{\pi m_e^4 c^5}{3h^3} = 6.00228\times 10^{22}~\mathrm{erg}~\mathrm{cm}^{-3}</math><br />
<br />
<font size="-1">
Reference (original): [http://adsabs.harvard.edu/abs/1935MNRAS..95..207C Chandraskehar, S. (1935)]<br />
Reference (recent): See Appendix of [http://adsabs.harvard.edu/abs/2009ApJS..184..248E Even & Tohline (2009)]<br />
Reference (authoritative book): [<b>[[Appendix/References#C67|<font color="red">C67</font>]]</b>]
</font>
</td>
<td>
[[Template:Math/C_FermiPressure|C_FermiPressure]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_FermiDensity }}
</td>
<td>
<font color="green">Characteristic Fermi density</font>;
<math>\frac{B_\mathrm{F}}{\mu_e} \equiv \frac{8\pi m_p}{3} \biggl( \frac{m_e c}{h} \biggr)^3 = 9.81011\times 10^{5}~\mathrm{g}~\mathrm{cm}^{-3}</math><br />
<br />
<font size="-1">
Reference (original): [http://adsabs.harvard.edu/abs/1935MNRAS..95..207C Chandraskehar, S. (1935)]<br />
Reference (recent): See Appendix of [http://adsabs.harvard.edu/abs/2009ApJS..184..248E Even & Tohline (2009)]<br />
Reference (authoritative book): [<b>[[Appendix/References#C67|<font color="red">C67</font>]]</b>]
</font>
</td>
<td>
[[Template:Math/C_FermiDensity|C_FermiDensity]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_RadiationConstant}}
</td>
<td>
<font color="green">Radiation [density] constant</font>;   
[http://scienceworld.wolfram.com/physics/RadiationConstant.html Authoritative Value] <br />
<math>a_\mathrm{rad} \equiv \frac{8\pi^5}{15}\frac{k^4}{(hc)^3} = 7.56576\times 10^{-15}~\mathrm{erg}~\mathrm{cm}^{-3}~\mathrm{K}^{-4}</math><br />
NOTE: <math>a_\mathrm{rad} = 4\sigma_\mathrm{SB}/c</math>, where <math>\sigma_\mathrm{SB}</math> is the [https://en.wikipedia.org/wiki/Stefan–Boltzmann_constant Stefan-Boltzmann constant]; see, for example, p. 428 of [[Appendix/References#HK94|[<b><font color="red">HK94</font></b>]]].
</td>
<td>
[[Template:Math/C_RadiationConstant|C_RadiationConstant]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_ElectronTemperature}}
</td>
<td>
<font color="green">Temperature associated with the rest-mass energy of the electron</font>;   
[[SR/PressureCombinations#Normalized_Ideal-Gas_Pressure|Context of Definition]] <br />
<math>T_e \equiv \frac{m_e c^2}{k} = 5.9381\times 10^{9}~\mathrm{K}</math><br />
</td>
<td>
[[Template:Math/C_ElectronTemperature|C_ElectronTemperature]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_ElectronCharge }}
</td>
<td>
<font color="green">Charge on an electron</font>;   
[http://en.wikipedia.org/wiki/Charge_of_electron Authoritative Value]
<br />
The cgs units (statcoulombs) are equivalent to <math>(\mathrm{g}~\mathrm{cm}^3~\mathrm{s}^{-2})^{1/2}</math>
</td>
<td>
[[Template:Math/C_ElectronCharge|C_ElectronCharge]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_FineStructureConstant}}
</td>
<td>
<font color="green">Fine structure constant</font> (dimensionless);   
[http://en.wikipedia.org/wiki/Fine-structure_constant Authoritative Value] <br />
<math>\alpha_\mathrm{fs} \equiv \frac{e^2}{\hbar c} = \frac{1}{137.0359997}</math><br />
</td>
<td>
[[Template:Math/C_FineStructureConstant|C_FineStructureConstant]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/C_ThompsonCrossSection}}
</td>
<td>
<font color="green">Thompson cross-section</font>;   
[http://en.wikipedia.org/wiki/Thompson_scattering Authoritative Value]
<br />
<math>\sigma_T \equiv \frac{8\pi}{3} \biggl(\frac{\alpha_\mathrm{fs} \hbar}{m_e c} \biggr)^2 = 0.6652458\times 10^{-24}~\mathrm{cm}^2</math><br />
</td>
<td>
[[Template:Math/C_ThompsonCrossSection|C_ThompsonCrossSection]]
</td>
<td align="center">
 
</td>
</tr>
</table>
</div>

==Variables==

<div align="center">
<table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue">
<tr>
<td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
{{ Math/<i><font color="red">Template_Name</font></i> }}</center>
</td>
</tr>
<tr>
<th width="8%">
<font color="red">Symbol</font>
</th>
<th>
<font color="red">Definition</font>
</th>
<th width="25%">
<font color="red">Template_Name</font>
</th>
<th width="10%">
<font color="red">Unicode</font>
</th>
</tr>

<tr>
<td align="center">
{{ Math/VAR_NumberDensity01 }}
</td>
<td>
<font color="green">Number density of gas particles</font>;    units of "1/volume"
</td>
<td>
[[Template:Math/VAR_NumberDensity01|VAR_NumberDensity01]]
</td>
<td align="center">
x004E
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_Density01}}
</td>
<td>
<font color="green">Mass density</font>;    units of "mass/volume"
</td>
<td>
[[Template:Math/VAR_Density01|VAR_Density01]]
</td>
<td align="center">
x03C1
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_SpecificVolume01}}
</td>
<td>
<font color="green">Specific Volume</font> = 1/{{ Math/VAR_Density01 }};    units of "volume/mass"
</td>
<td>
[[Template:Math/VAR_SpecificVolume01|VAR_SpecificVolume01]]
</td>
<td align="center">
x0056
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_NewtonianPotential01}}
</td>
<td>
<font color="green">Newtonian gravitational potential</font>;    units of "energy/mass" or "velocity-squared"
</td>
<td>
[[Template:Math/VAR_NewtonianPotential01|VAR_NewtonianPotential01]]
</td>
<td align="center">
x03A6
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_Enthalpy01}}
</td>
<td>
<font color="green">Enthalpy</font>;    units of "energy/mass" or "velocity-squared"
</td>
<td>
[[Template:Math/VAR_Enthalpy01|VAR_Enthalpy01]]
</td>
<td align="center">
x0048
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_Pressure01}}
</td>
<td>
<font color="green">Pressure</font>;    units of "force/area" or "energy/volume"
</td>
<td>
[[Template:Math/VAR_Pressure01|VAR_Pressure01]]
</td>
<td align="center">
x0050
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_SpecificInternalEnergy01}}
</td>
<td>
<font color="green">Specific internal energy</font>;    units of "energy/mass" or "velocity-squared"
</td>
<td>
[[Template:Math/VAR_SpecificInternalEnergy01|VAR_SpecificInternalEnergy01]]
</td>
<td align="center">
x03B5
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_SpecificEntropy01}}
</td>
<td>
<font color="green">Specific entropy</font>;
</td>
<td>
[[Template:Math/VAR_SpecificEntropy01|VAR_SpecificEntropy01]]
</td>
<td align="center">
x0073
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_Time01}}
</td>
<td>
<font color="green">Time</font>
</td>
<td>
[[Template:Math/VAR_Time01|VAR_Time01]]
</td>
<td align="center">
x0074
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_Temperature01}}
</td>
<td>
<font color="green">Temperature</font>;    units of "Kelvin"
</td>
<td>
[[Template:Math/VAR_Temperature01|VAR_Temperature01]]
</td>
<td align="center">
x0054
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_VelocityVector01}}
</td>
<td>
<font color="green">Euclidean 3-space velocity vector</font>;    units of "length/time"
</td>
<td>
[[Template:Math/VAR_VelocityVector01|VAR_VelocityVector01]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/VAR_PositionVector01}}
</td>
<td>
<font color="green">Euclidean 3-space position vector</font>
</td>
<td>
[[Template:Math/VAR_PositionVector01|VAR_PositionVector01]]
</td>
<td align="center">
 
</td>
</tr>
</table>
</div>

==Model Parameters==

<div align="center">
<table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue">
<tr>
<td colspan=4>
To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center>
{{ Math/<i><font color="red">Template_Name</font></i> }}</center>
</td>
</tr>
<tr>
<th width="8%">
<font color="red">Symbol</font>
</th>
<th>
<font color="red">Definition</font>
</th>
<th width="25%">
<font color="red">Template_Name</font>
</th>
<th width="10%">
<font color="red">Unicode</font>
</th>
</tr>

<tr>
<td align="center">
{{ Math/MP_AdiabaticIndex }}
</td>
<td>
<font color="green">Adiabatic Index (or Ratio of Specific Heats)</font>; dimensionless   
[http://en.wikipedia.org/wiki/Heat_capacity_ratio Wikipedia Discussion]
</td>
<td>
[[Template:Math/MP_AdiabaticIndex|MP_AdiabaticIndex]]
</td>
<td align="center">
 
</td>
</tr>

<tr>
<td align="center">
{{ Math/MP_MeanMolecularWeight }}
</td>
<td>
<font color="green">Mean molecular weight</font>; dimensionless;   
defined such that {{ Math/MP_MeanMolecularWeight }} = {{ Math/VAR_Density01 }} / ({{ Math/C_AtomicMassUnit }}{{Template:Math/VAR_NumberDensity01}}).
</td>
<td>
[[Template:Math/MP_MeanMolecularWeight | MP_MeanMolecularWeight]]
</td>
<td align="center">
x03BC
</td>
</tr>

<tr>
<td align="center">
{{ Math/MP_ElectronMolecularWeight }}
</td>
<td>
<font color="green">Molecular weight of electrons</font>; dimensionless; <br />
defined such that {{ Math/MP_ElectronMolecularWeight }} = {{ Math/VAR_Density01 }} / ({{ Math/C_AtomicMassUnit }} <math>N_e</math>), where <math>N_e</math> is the number density of electrons.
</td>
<td>
[[Template:Math/MP_ElectronMolecularWeight | MP_ElectronMolecularWeight]]
</td>
<td align="center">
x03BC
</td>
</tr>

<tr>
<td align="center">
{{ Math/MP_PolytropicIndex }}
</td>
<td>
<font color="green">Polytropic Index</font>; dimensionless   
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
</td>
<td>
[[Template:Math/MP_PolytropicIndex | MP_PolytropicIndex]]
</td>
<td align="center">
x006E
</td>
</tr>

<tr>
<td align="center">
{{ Math/MP_PolytropicConstant }}
</td>
<td>
<font color="green">Polytropic Constant</font>; dimensions depend on choice of {{ Math/MP_PolytropicIndex }}   
[http://en.wikipedia.org/wiki/Polytrope Wikipedia Discussion]
</td>
<td>
[[Template:Math/MP_PolytropicConstant | MP_PolytropicConstant]]
</td>
<td align="center">
 
</td>
</tr>

</table>
</div>

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