Special Distribution of Blackbody Radiation - Wien's Law

Physics

law

Wien's displacement Law

Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature.

where T is the absolute temperature in kelvin. b is a constant of proportionality called Wien's displacement constant, equal to

diagram

Spectrum of blackbody radiation vs wavelength at different temperatures

Intensity increases with temperature and peak wavelength decreases with temperature

definition

Heat detection devices

Bolometer and Thermopile are two devices to measure radiation.
Bolometer
It is based on the working principle of the Wheatstone bridge. A thin foil of platinum is cut into strips in a grid like pattern. Four such identical grids are taken to form a Wheatstone bridge with a battery and a galvanometer connected. Grids 1 and 4 are allowed to fall radiation upon whereas grids 2 and 3 are protected from radiation. At balance condition the resistances of the grids are related as:
where are the resistances of the grid.
As temperature increases on radiation, and increases but the product remains constant. This brings about a deflection in the galvanometer which is a measure of radiation.
Thermopile
It works on the principle of Seeback effect. A thermopile s composed of a number of thermocouples made from bismuth and antimony in a series connection to increase the sensitivity of the system. The free ends are connected to a galvanometer. The junctions are arranged in such a way that all the hot junctions lie on a plane face and all the cold junctions lie on the opposite plane face.The face of the hot junctions is blackened and exposed to radiation while the other face is shielded.  A metallic cone generally concentrates the radiation on the hot face. The radiation is measured by the deflection in the galvanometer.

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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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