This document discusses several laws relating to the radiation of heat, including: 1) Kirchhoff's law, which states that the emission of a body at a given wavelength and temperature is equal to the ratio of the emissivity and blackbody emission. Real objects emit less radiation than black bodies. 2) Wien's law, which says the dominant wavelength at which a blackbody emits radiation is inversely proportional to its temperature. 3) The Stefan-Boltzmann law, stating that a blackbody's total energy flux is directly proportional to the fourth power of its temperature.

1. PROCESS HEAT
TRANSFER
 LAWS OF RADIATION
By: PARAS H BORICHA
(130280105004)

2. WHAT
IS
RADIATION???

3. • Radiation is the transfer of energy by rapid
oscillations of electromagnetic fields.
• The most important general characteristic is
its wavelength .
• Radiation travels through space at the speed
of light
(3 x 108 m s-1) or 670,616,630 MPH.

4. LAWS
OF
RADIATION

5. A black body , by definition, absorbs radiation at all wavelengths
completely. Real objects are never entirely “black” – the cannot absorb all
wavelengths completely, but show a wavelength-dependent
absorptivity ε(λ) (which is < 1).
According to Kirchhoff’s law (Gustav Kirchhoff, 1859) the Emission of a
body, Eλ (in thermodynamic equilibrium) is:
For a given wavelength and temperature, the ratio of the Emission and the
absorptivity equals the black body emission.
This shows also, that objects emit radiation in the same parts of the
spectrum in which they absorb radiation.
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Atmo II 84
Kirchhoff’s Law

6. We rearrange Kirchhoff’s law and see:
At a given temperature, real objects emit less radiation than a black body
(since ε < 1). Therefore we can regard ε(λ) also as emissivity. Quite often
you will thus find Kirchhoff’s law in the form:
Emissivity = Absorptivity
Important: it applies wavelength-dependent.
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Kirchhoff’s Law
Atmo II 85
In the infrared all naturally occurring surfaces are – in very good
approximation – “black” – even snow! (which is – usually – not
black at all in the visible part of the spectrum).
For the Earth as a whole (in the IR): ε = 0.95 („gray body“)

7. Wien’s law and the Stefan-Boltzmann law are
useful tools for analyzing glowing objects like stars
• A blackbody is a hypothetical
object that is a perfect
absorber of electromagnetic
radiation at all wavelengths
• Stars closely approximate the
behavior of blackbodies, as do
other hot, dense objects
• The intensities of radiation
emitted at various
wavelengths by a blackbody
at a given temperature are
shown by a blackbody curve

8. Wien’s Law
Wien’s law states that the
dominant wavelength at which a
blackbody emits electromagnetic
radiation is inversely proportional
to the Kelvin temperature of the
object

10. Stefan-Boltzmann Law
• The Stefan-Boltzmann law states that a
blackbody radiates electromagnetic waves
with a total energy flux E directly
proportional to the fourth power of the
Kelvin temperature T of the object:
E = T4

11. Planck’s Law
According to Planck’s Law (Max Planck, 1900) the energy emitted by a
black body (un-polarized radiation) per time, area, solid angle and wave
length λ equals:
c0 = Speed of light (in vacuum) = 299 792 458 m s–1
h = Planck constant = 6.626 069 57·10–34 Js
kB = Boltzmann constant = 1.380 6488·10–23 J K-1
According to our last slides this has to be – right:
Spectral radiance with respect to wavelength [Wm–2 sr–1 m–1]
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12. Planck’s Law (last slide) refers to un-polarized radiation per solid angle. In
case of linear polarization we would just get half of it. If you should miss a
factor π – this comes be integrating over the half space. Planck‘s law often
comes in frequency formulation:
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1exp
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dBB 2
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Planck’s Law