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Physical Constants, Variables, and Model Parameters

Whitworth's (1981) Isothermal Free-Energy Surface
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To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...
{{ User:Tohline/Math/Template_Name }}

Symbol

Definition

Template_Name

Unicode

Physical Constants:

<math>~c</math>

Speed of light;    Authoritative Value

C_SpeedOfLight

x0063

<math>~G</math>

Newtonian gravitational constant;    Authoritative Value

C_GravitationalConstant

x0047

<math>~h</math>

Planck constant;    Authoritative Value
Note: <math>\hbar \equiv \frac{h}{2\pi}</math>

C_PlanckConstant

x0068

<math>~k</math>

Boltzmann constant;    Authoritative Value

C_BoltzmannConstant

x006B

<math>~N_A</math>

Avogadro constant;    Authoritative Value

C_AvogadroConstant

 

<math>~m_e</math>

Electron mass;    Authoritative Value

C_ElectronMass

 

<math>~m_p</math>

Proton mass;    Authoritative Value

C_ProtonMass

 

<math>~m_u</math>

Atomic mass unit;    Authoritative Value;    NOTE: <math>m_p/m_u = 1.007276</math>

C_AtomicMassUnit

 

<math>~\Re</math>

Gas constant = <math>~k</math><math>~N_A</math> = 1.007276 <math>~k</math>/<math>~m_p</math>;    Authoritative Value

C_GasConstant

x211C

<math>~A_\mathrm{F}</math>

Characteristic Fermi pressure;
<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>

Reference (original): Chandraskehar, S. (1935)
Reference (recent): See Appendix of Even & Tohline (2009)
Reference (authoritative book): [C67]

C_FermiPressure

 

<math>~B_\mathrm{F}</math>

Characteristic Fermi density; <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>

Reference (original): Chandraskehar, S. (1935)
Reference (recent): See Appendix of Even & Tohline (2009)
Reference (authoritative book): [C67]

C_FermiDensity

 

<math>~a_\mathrm{rad}</math>

Radiation constant;    Authoritative Value
<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>

C_RadiationConstant

 

<math>~T_e</math>

Temperature associated with the rest-mass energy of the electron;    Context of Definition
<math>T_e \equiv \frac{m_e c^2}{k} = 5.9381\times 10^{9}~\mathrm{K}</math>

C_ElectronTemperature

 

<math>~e</math>

Charge on an electron;    Authoritative Value
The cgs units (statcoulombs) are equivalent to <math>(\mathrm{g}~\mathrm{cm}^3~\mathrm{s}^{-2})^{1/2}</math>

C_ElectronCharge

 

<math>~\alpha_\mathrm{fs}</math>

Fine structure constant (dimensionless);    Authoritative Value
<math>\alpha_\mathrm{fs} \equiv \frac{e^2}{\hbar c} = \frac{1}{137.0359997}</math>

C_FineStructureConstant

 

<math>~\sigma_T</math>

Thompson cross-section;    Authoritative Value
<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>

C_ThompsonCrossSection

 

Variables:

<math>~n_g</math>

Number density of gas particles;    units of "1/volume"

VAR_NumberDensity01

x004E

<math>~\rho</math>

Mass density;    units of "mass/volume"

VAR_Density01

x03C1

<math>~V</math>

Specific Volume = 1/<math>~\rho</math>;    units of "volume/mass"

VAR_SpecificVolume01

x0056

<math>~\Phi</math>

Newtonian gravitational potential;    units of "energy/mass" or "velocity-squared"

VAR_NewtonianPotential01

x03A6

<math>~H</math>

Enthalpy;    units of "energy/mass" or "velocity-squared"

VAR_Enthalpy01

x0048

<math>~P</math>

Pressure;    units of "force/area" or "energy/volume"

VAR_Pressure01

x0050

<math>~\epsilon</math>

Specific internal energy;    units of "energy/mass" or "velocity-squared"

VAR_SpecificInternalEnergy01

x03B5

<math>~s</math>

Specific entropy;

VAR_SpecificEntropy01

x0073

<math>~t</math>

Time

VAR_Time01

x0074

<math>~T</math>

Temperature;    units of "Kelvin"

VAR_Temperature01

x0054

<math>~\vec{v}</math>

Euclidean 3-space velocity vector;    units of "length/time"

VAR_VelocityVector01

 

<math>~\vec{x}</math>

Euclidean 3-space position vector

VAR_PositionVector01

 

Model Parameters:

<math>~\gamma_\mathrm{g}</math>

Adiabatic Index (or Ratio of Specific Heats); dimensionless    Wikipedia Discussion

MP_AdiabaticIndex

 

<math>~\bar{\mu}</math>

Mean molecular weight; dimensionless;    defined such that <math>~\bar{\mu}</math> = <math>~\rho</math>/(<math>~m_u</math><math>~n_g</math> ).

MP_MeanMolecularWeight

x03BC

<math>~\mu_e</math>

Molecular weight of electrons; dimensionless;
defined such that <math>~\mu_e</math> = <math>~\rho</math>/(<math>~m_u</math> <math>N_e</math>), where <math>N_e</math> is the number density of electrons.

MP_ElectronMolecularWeight

x03BC

<math>~n</math>

Polytropic Index; dimensionless    Wikipedia Discussion

MP_PolytropicIndex

x006E

<math>~K_\mathrm{n}</math>

Polytropic Constant; dimensions depend on choice of <math>~n</math>    Wikipedia Discussion

MP_PolytropicConstant

 

 

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation