PROCESS HEAT

TRANSFER

LAWS OF RADIATION

By: PARAS H BORICHA

(130280105004)

WHAT

IS

RADIATION???

• 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.

LAWS

OF

RADIATION

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.

),()(ε

),(T

T

BE

Atmo II 84

Kirchhoff’s Law

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.

)()()( TBTE ,ε,

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“)

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

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

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

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]

1exp

125

2

Tk

hc

hcTB

B

0

0),(

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:

),(),(

TBTB

1exp

122

3

Tk

hc

hTB

B

0

),(

0cB

d

dBB 2

0c

Planck’s Law