Stefan Boltzmann

Post on 18-Apr-2015

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Stefan, Boltzmann, constant,

Transcript of 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

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.

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.

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

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.