Buckley Rumford Fireplaces
Radiant Heating Formulas


Planck's Law
Stephan-Boltzman Law
Wien's Law
Kirchhoff's Law
Planck's Law of Black Body Radiation
From Wikipedia, the free encyclopedia.

Energy transferred from a warm body to a cooler body by radiation is described by Planck's Law of Black Body Radiation which describes radiant energy as a function of wave length. This equation generates the blackbody curves.


ν is the frequency
I(ν)δν is the amount of energy per unit surface per unit time per unit solid angle emitted in the frequency range between ν and ν+δν;
h is Planck's constant,
c is the speed of light and
k is Boltzmann's constant.

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Stephan-Boltzman Law
From Solaronic, Inc.)

Radiant energy is proportional to the fourth power of the absolute temperature of the source. The amount of radiation produced by a perfect radiator is expressed by the Stephan-Boltzman Law, where:

For ordinary objects, non-perfect radiators, Q is reduced by multiplication of the object's emissive power (always less than one). And emissivity changes with temperature. But, for the most part, the amount of radiatiant energy is a function of the fourth pawer of the absolute temperature of the source of radiation. Thus, at normal temperatures the amount of infra-red radiation produced by an object is relatively low, but as the temperature is increased, radiation increases significantly.

Stephan-Boltzman Law gives the total energy emitted, but as the temperature rises, more of the energy is emitted at shorter wavelengths as given by Wein's Displacement Law and shown by the Planck blackbody curves.. Thus, if you double the absolute temperature, you get 2 to the 4th or 16 times the TOTAL energy out, but more of this energy is output at shorter wavelengths and may not be felt as heat. (We normally consider the 8 to 12 micron region as thermal infrared) - Hoffamn.

For example: An object at 80 deg.F (540 deg. absolute temperature Rankine) with an emissive power of 0.85 will produce 124 BTUH/sq.ft. When its absolute temperature is doubled to 1080 deg. (620 deg.F, which is about the temperature of a very hot glass door) its output is increased sixteen fold to 1,984 BTUH/sq.ft. If its absolute temperature is quadrupled to 2160 deg. (1,700 deg.F which is not a very hot wood fire) its output increases two hundred and fifty six fold to 31,744 BTUH/sq.ft.

An open fire radiates at about 16 times more energy than the same fire would produce behind glass doors.

Wikipedia on Stefan-Boltzmann law
Stefan-Boltzmann Law with practical examples and calculators.
discussion with Hoffman.
Fahrenheit to Celsius Converter

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Wien's Law

Wave length is inversely proportional to temperature of the source. The relationship of the wavelength of maximum intensity of a black body to its absolute temperature is expressed by Wien's law.

Wien's Law

L max = a/T

a = 2898 if L is measured in microns

From the Amherst Astronomy Assoc.
with thanks to Mark Godwin at GSSM

Note: Our sun's energy at T=6000 K peaks at 0.5 microns (where our eye response also peaks).

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Kirchhoff's Law

emissivity = absorbtance at any given wavelength and temperature

Thus "a good absorber is a good emitter" (which has to be true for the object to stay at the same temperature)

This can be expanded into the "common sense" equation that the total incident energy must equal the sum of the absorbed, reflected, and transmitted energy.

Energy = energy absorbed + energy reflected + energy transmitted

Kirchhoff's law is really just common sense: When radiant energy hits any particular material it has to do one of three things:
    1) Be absorbed (a perfect black body with emissivity of 1 absorbes all the radiant energy)
    2) Be reflected (the opposite of a perfect black body - a material with low emissivity)
    3) Pass through the material (transparancy)

The energy of the raditaion absorbed, reflected and transmitted through the material must equal the energy hitting the material.

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Absolute Zero

The lowest possible temperature allowed by the laws of thermodynamics. At this temperature, molecules would possess the absolute minimum kinetic energy allowed by quantum mechanics (the Heisenberg Uncertainty Principle places a greater than zero lower limit on the kinetic energy of molecules). It is equivalent to -273.15 deg.C or 0K (kelvin). At absolute zero, the entropy of any system vanished.

Absolute Zero in K=C+273.16
Absolute Zero in Rankine=F+459.69

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Radiant Heat
Buckley Rumford Fireplaces
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