Stefan Boltzmann

7

description

Stefan, Boltzmann, constant,

Transcript of Stefan Boltzmann

Page 1: Stefan Boltzmann
Page 2: Stefan Boltzmann

•The energy transfer by heat flow due to presence of temperature gradient in a system is known as Heat transfer.•There are three modes of heat transfer-conduction, convection and radiation.•Thermal radiation refers to heat energy emitted by bodies because of their temperature. All bodies at a temperature above absolute zero emit thermal radiation

Page 3: Stefan Boltzmann

The concept of blackbody is an idealized situation that serves to compare the radiation properties of real bodies.

A blackbody is considered to absorb all incident radiation from all directions at all wavelengths without reflecting , transmitting or scattering it.

For a given temperature and wavelength no other body can emit more radiation than a blackbody.

Page 4: Stefan Boltzmann
Page 5: Stefan Boltzmann

Spectral blackbody radiation intensity Ibλ(T) is given by Planck`s formula

Ibλ(T) =c1/λ5{exp(c2/λT)-1},where c1 and c2 are constants.

Here Ibλ(T) represents the radiation energy emitted by a blackbody at temperature T streaming through a unit area perpendicular to the direction of propagation of per unit wavelength about the wavelength λ per unit solid angle about the direction of propagation of the beam.

Page 6: Stefan Boltzmann

Spectral blackbody emissive power (Ebλ) is given by the amount of radiation energy emitted per unit area of the blackbody per unit wavelength about the wavelength λ at temperature T in all direction into hemispherical space.

Blackbody emissive power is given by Eb(T)=0∫

∞ Ebλ(T)dλ

Page 7: Stefan Boltzmann

Using geometry and calculus we can easily proveEbλ(T)=πIbλ(T).

So Eb(T)=0∫∞ Ebλ(T)dλ= π

0∫∞ Ibλ(T)dλ=σT4 .

This is known as Stefan Boltzmann Law and σ is called Stefan Boltzmann constant. It`s numerical value is 5.67*10-8 W/m2K4.