[2.13.4] An expression representing the spectral radiance of a blackbody as a function of the wavelength and temperature. This law is commonly expressed by the formula:

where:

*L*= the spectral radiance

_{λ}d

*I*= the spectral radiant intensity

_{λ}d

*A’*= the projected area (d

*A*cos

*θ*) of the aperture of the blackbody

*e*= the base of natural logarithms ( approx. 2.71828)

*Τ*= absolute temperature

*c*and

_{1L}*c*are constants designated as the first and second radiation constants.

_{2}*Note:* The designation *c _{1L}* is used to indicate that the equation in the form given here refers to the radiance

*L*, or to the intensity

*I*per unit projected area

*A’*, of the source. Numerical values are commonly given not for

*c*but for

_{1L}*c*, which applies to the total flux radiated from a blackbody aperture (that is, in a hemisphere [2π steradians]) so that, with the Lambert cosine law taken into account,

_{1}*c*π

_{1}=*c*

*.*

_{1L}The currently recommended value of *c1* is 3.741832 x 10^{-16} W·m^{2}, or 3.741832 x 10^{-12} W*·*cm^{2}.

Then *c _{1L}* is 1.191062 x 10

^{-16}W

*·*m

^{2}/sr, or 1.191062 x 10

^{-12}W·cm

^{2}/

*sr*.

If, as is more convenient, wavelengths are expressed in micrometers and area in square centimeters, *c _{1L}* = 1.191062 x 10

^{4}W·μm

^{4}/(cm

^{2}·sr), with

*L*being given in W

_{λ}*/(*cm

^{2}·sr·μm).

The currently recommended value of *c _{2}* is 1.438786 x 10

^{-2}m·K.[note]Values of radiation constants from NBS Special Publication 398.[/note]

The Planck law in the following form gives the energy radiated from the blackbody in a given wavelength interval (λ_{1} – λ_{2}):

*A*is the area of the radiation aperture or surface in square centimeters,

*t*is time in seconds,

*λ*is wavelength in micrometers, and

*c*

_{1}= 3.741832 x 10

^{4}W

*·*μm

^{4}/cm

^{2}, then

*Q*is the total energy in watt seconds (joules) emitted from this area (that is, in the solid angle 2π) in time

*t*, within the wavelength interval (

*λ*–

_{1}*λ*). « Back to Definitions Index

_{2}