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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:

~c

Speed of light;    Authoritative Value

C_SpeedOfLight

x0063

~G

Newtonian gravitational constant;    Authoritative Value

C_GravitationalConstant

x0047

~h

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

C_PlanckConstant

x0068

~k

Boltzmann constant;    Authoritative Value

C_BoltzmannConstant

x006B

~N_A

Avogadro constant;    Authoritative Value

C_AvogadroConstant

 

~m_e

Electron mass;    Authoritative Value

C_ElectronMass

 

~m_p

Proton mass;    Authoritative Value

C_ProtonMass

 

~m_u

Atomic mass unit;    Authoritative Value;    NOTE: mp / mu = 1.007276

C_AtomicMassUnit

 

~\Re

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

C_GasConstant

x211C

~A_\mathrm{F}

Characteristic Fermi pressure;
A_\mathrm{F} \equiv \frac{\pi m_e^4 c^5}{3h^3} = 6.00228\times 10^{22}~\mathrm{erg}~\mathrm{cm}^{-3}

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

C_FermiPressure

 

~B_\mathrm{F}

Characteristic Fermi density; \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}

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

C_FermiDensity

 

~a_\mathrm{rad}

Radiation constant;    Authoritative Value
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}

C_RadiationConstant

 

~T_e

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

C_ElectronTemperature

 

~e

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

C_ElectronCharge

 

~\alpha_\mathrm{fs}

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

C_FineStructureConstant

 

~\sigma_T

Thompson cross-section;    Authoritative Value
\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

C_ThompsonCrossSection

 

Variables:

~n_g

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

VAR_NumberDensity01

x004E

~\rho

Mass density;    units of "mass/volume"

VAR_Density01

x03C1

~V

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

VAR_SpecificVolume01

x0056

~\Phi

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

VAR_NewtonianPotential01

x03A6

~H

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

VAR_Enthalpy01

x0048

~P

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

VAR_Pressure01

x0050

~\epsilon

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

VAR_SpecificInternalEnergy01

x03B5

~s

Specific entropy;

VAR_SpecificEntropy01

x0073

~t

Time

VAR_Time01

x0074

~T

Temperature;    units of "Kelvin"

VAR_Temperature01

x0054

~\vec{v}

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

VAR_VelocityVector01

 

~\vec{x}

Euclidean 3-space position vector

VAR_PositionVector01

 

Model Parameters:

~\gamma_\mathrm{g}

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

MP_AdiabaticIndex

 

~\bar{\mu}

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

MP_MeanMolecularWeight

x03BC

~\mu_e

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

MP_ElectronMolecularWeight

x03BC

~n

Polytropic Index; dimensionless    Wikipedia Discussion

MP_PolytropicIndex

x006E

~K_\mathrm{n}

Polytropic Constant; dimensions depend on choice of ~n    Wikipedia Discussion

MP_PolytropicConstant

 

 

Whitworth's (1981) Isothermal Free-Energy Surface

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