Planck's Law

Functions
template<typename T >
T	EGXPhys::PlancksLaw (const T wavelengthInm, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{\lambda}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavelength, \(\lambda\), for a unit surface area of the black body. \[ B_{\lambda} = \dfrac{2 h c^2}{\lambda^5} \dfrac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromFrequency (const T frequencyInHz, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{\nu}\), in watts per steradian meter squared hertz of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific frequency, \(\nu\), for a unit surface area of the black body. \[ B_{\nu} = \dfrac{2 h \nu^3}{c^2} \dfrac{1}{e^{\frac{h\nu}{k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromWavelength (const T wavelengthInm, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{\lambda}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavelength, \(\lambda\), for a unit surface area of the black body. \[ B_{\lambda} = \dfrac{2 h c^2}{\lambda^5} \dfrac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromWavenumber (const T wavenumberInInversem, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{\tilde {\nu }}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavenumber, \(\tilde {\nu }\), for a unit surface area of the black body. \[ B_{\tilde {\nu }} = 2 h c^2 \tilde {\nu }^3 \dfrac{1}{e^{\frac{hc \tilde {\nu }}{k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromAngularFrequency (const T angularFrequencyInRadiansPers, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{\omega}\), in watt radians per steradian meter squared hertz of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular frequency, \(\omega\), for a unit surface area of the black body. \[ B_{\omega} = \dfrac{\hbar \omega^3}{4\pi^3c^2} \dfrac{1}{e^{\frac{\hbar\omega}{k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromAngularWavelength (const T angularWavelengthInm, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{y}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular wavelength, /f$y/f$, for a unit surface area of the black body. \[ B_{y} = \dfrac{\hbar c^2}{4\pi^3y^5} \dfrac{1}{e^{\frac{\hbar c}{y k_B T}} - 1} \] . More...
template<typename T >
T	EGXPhys::PlancksLawFromAngularWavenumber (const T angularWavenumberInRadianPerm, const T surfaceTempretureInK)
	Calculates the spectral radiance, \(B_{k}\), in watts per steradian meter of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular wavenumber, \(k\), for a unit surface area of the black body. \[ B_{k} = \dfrac{\hbar c^2 k^3}{4\pi^3} \dfrac{1}{e^{\frac{\hbar c k}{k_B T}} - 1} \] . More...

Detailed Description

Function Documentation

PlancksLaw()

template<typename T >

T EGXPhys::PlancksLaw	(	const T	wavelengthInm,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{\lambda}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavelength, \(\lambda\), for a unit surface area of the black body.

\[ B_{\lambda} = \dfrac{2 h c^2}{\lambda^5} \dfrac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
wavelengthInm	\(\lambda\ (m)\) Wavelength at which to find spectral radiance at in meters.

Returns

\(B_{\lambda}\ ( \dfrac{W}{sr\ m^3})\) Spectral radiance of a black body at the wavelength, \(\lambda\), in watts per steradian meter cubed.

See also

PlancksLawFromWavelength() for alias.

SpectralRadianceFromWavelength for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.

PlancksLawFromAngularFrequency()

template<typename T >

T EGXPhys::PlancksLawFromAngularFrequency	(	const T	angularFrequencyInRadiansPers,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{\omega}\), in watt radians per steradian meter squared hertz of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular frequency, \(\omega\), for a unit surface area of the black body.

\[ B_{\omega} = \dfrac{\hbar \omega^3}{4\pi^3c^2} \dfrac{1}{e^{\frac{\hbar\omega}{k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
angularFrequencyInRadiansPers	\(\omega\ (\frac{rad}{Hz})\) Angular frequency at which to find spectral radiance at in radians per hertz.

Returns

\(B_{\omega}\ ( \dfrac{W Hz}{sr\ m^2 rad})\) Spectral radiance of a black body at the angular frequency, \(\omega\), in watt hertz per steradian meter squared radian.

See also

SpectralRadianceFromAngularFrequency for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.

PlancksLawFromAngularWavelength()

template<typename T >

T EGXPhys::PlancksLawFromAngularWavelength	(	const T	angularWavelengthInm,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{y}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular wavelength, /f$y/f$, for a unit surface area of the black body.

\[ B_{y} = \dfrac{\hbar c^2}{4\pi^3y^5} \dfrac{1}{e^{\frac{\hbar c}{y k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
angularWavelengthInm	\(y\ (m)\) Angular wavelength at which to find spectral radiance at in meters.

Returns

\(B_{y}\ ( \dfrac{W}{sr\ m^3})\) Spectral radiance of a black body at the angular wavelength, \(y\) in watts per steradian meter cubed.

See also

SpectralRadianceFromAngularWavelength for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.

PlancksLawFromAngularWavenumber()

template<typename T >

T EGXPhys::PlancksLawFromAngularWavenumber	(	const T	angularWavenumberInRadianPerm,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{k}\), in watts per steradian meter of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific angular wavenumber, \(k\), for a unit surface area of the black body.

\[ B_{k} = \dfrac{\hbar c^2 k^3}{4\pi^3} \dfrac{1}{e^{\frac{\hbar c k}{k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
angularWavenumberInRadianPerm	\(k\ (\frac{rad}{m})\) Angular wavenumber at which to find spectral radiance at in radians per meter.

Returns

\(B_{k}\ ( \dfrac{W}{sr\ m\ rad})\) Spectral radiance of a black body at the angular wavenumber, \(k\), in watts per steradian meter radian.

See also

SpectralRadianceFromAngularWavenumber for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromFrequency()

template<typename T >

T EGXPhys::PlancksLawFromFrequency	(	const T	frequencyInHz,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{\nu}\), in watts per steradian meter squared hertz of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific frequency, \(\nu\), for a unit surface area of the black body.

\[ B_{\nu} = \dfrac{2 h \nu^3}{c^2} \dfrac{1}{e^{\frac{h\nu}{k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
frequencyInHz	\(\nu\ (Hz)\) Frequency at which to find spectral radiance at in hertz.

Returns

\(B_{\nu}\ ( \dfrac{W}{sr\ m^2 Hz})\) Spectral radiance of a black body at the frequency, \(\nu\), in watts per steradian meter squared hertz.

See also

SpectralRadianceFromFrequency for alias.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.

PlancksLawFromWavelength()

template<typename T >

T EGXPhys::PlancksLawFromWavelength	(	const T	wavelengthInm,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{\lambda}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavelength, \(\lambda\), for a unit surface area of the black body.

\[ B_{\lambda} = \dfrac{2 h c^2}{\lambda^5} \dfrac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
wavelengthInm	\(\lambda\ (m)\) Wavelength at which to find spectral radiance at in meters.

Returns

\(B_{\lambda}\ ( \dfrac{W}{sr\ m^3})\) Spectral radiance of a black body at the wavelength, \(\lambda\), in watts per steradian meter cubed.

See also

PlancksLaw for alias.

SpectralRadiance for alias.

SpectralRadianceFromWavelength for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavenumber for spectral radiance calulations using wavenumber.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.

PlancksLawFromWavenumber()

template<typename T >

T EGXPhys::PlancksLawFromWavenumber	(	const T	wavenumberInInversem,
		const T	surfaceTempretureInK
	)

Calculates the spectral radiance, \(B_{\tilde {\nu }}\), in watts per steradian meter cubed of a black body from the surface tempreture, \(T\) of the black body using Plank's Law. The spectral radience is the amount of power emmited per steradian at a specific wavenumber, \(\tilde {\nu }\), for a unit surface area of the black body.

\[ B_{\tilde {\nu }} = 2 h c^2 \tilde {\nu }^3 \dfrac{1}{e^{\frac{hc \tilde {\nu }}{k_B T}} - 1} \]

.

See https://en.wikipedia.org/wiki/Planck%27s_law

Parameters

surfaceTempretureInK	\(T\ (K)\) Surface tempreture of the black body in kelvin.
wavenumberInInversem	\(\tilde {\nu }\ (\frac{1}{m})\) Wavemnumber at which to find spectral radiance at in inverse meters.

Returns

\(B_{\tilde {\nu }}\ ( \dfrac{W}{sr\ m})\) Spectral radiance of a black body at the wavenumber, \(\tilde {\nu }\) in watts per steradian meter.

See also

SpectralRadianceFromWavenumber for alias.

PlancksLawFromFrequency for spectral radiance calulations using frequency.

PlancksLawFromWavelength for spectral radiance calulations using wavelenght.

PlancksLawFromAngularFrequency for spectral radiance calulations using angular frequency.

PlancksLawFromAngularWavelength for spectral radiance calulations using angular wavelenght.

PlancksLawFromAngularWavenumber for spectral radiance calulations using angular wavenumber.