Stefan Boltzmann Law

Physics

formula

Energy emitted per unit time by a body


where u is the energy emitted by a body per unit time,
e is the emissivity
is the Stefan-boltzmann constant
A is the surface area and
T is the temperature

definition

Thermal energy lost per unit time due to radiation

Suppose a body of surface area A at an absolute temperature is kept in a surrounding having a lower temperature  . The net rate of loss of thermal energy from the body due to radiation is 

    if the temperature difference is small

definition

Intensity at a finite distance from the source

Intensity of thermal radiation decays as:

where
Intensity at a distance from the reference point
Intensity at the reference point

Example:
Find the ratio of amplitudes of radiation emitted by a cylindrical source at distances and from its axis.
Solution:
Let the intensity of the cylindrical source be
The intensity at a distance is given by: 
The intensity at a distance is given by: 

where Amplitude

REVISE WITH CONCEPTS

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Important Questions

The temperature of equal masses of three different liquids and are and respectively. The temperature when and are mixed is and when and are mixed it is . What should be the temperature when and are mixed?

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A body cools from C to C in minutes. Calculate the time it takes to cool from C to C. The temperature of the surroundings is C.

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A black body at a temperature of radiates heat energy at the rate . At a temperature of , the rate of heat radiated per unit area in will be:

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A spherical black body with a radius of 12cm radiates 450W power at 500K. If the radius were halved and the temperature doubled, the power radiated in watts would be :

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State Kirchhoff's law of radiation and prove it theoretically.

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Certain quantity of water cools from to in the first minutes and to in the next minutes. The temperature of the surroundings is ;

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A pan filled with hot food cools from to in minutes. When the room temperature is . How long will it cool from to ?

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A body cools down from to in Minutes when the temperature of surrounding is . The temperature of the body after next minutes will be:

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A sphere , a cube and a thin circular plate,all of same materials and same mass, are initially heated to same high temperature. 

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The plots of intensity versus wavelength for three black bodies at temperatures  and  respectively are shown in fig. Their temperatures are such that:

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