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The relationship (Wavelength) _{MAX} T = constant, between the temperature of a black body and the wavelength at which maximum value of monochromatic emissive power occurs is known as
This is the Wien’s law. From the spectral distribution of black body emissive power, it is apparent that the wavelength associated with maximum rate of emission depends up on the absolute temperature of the radiating surface.
A body at 500 K cools by radiating heat to ambient atmosphere maintained at 300 K. When the body has cooled to 400 K, the cooling rate as a percentage of original rate is about
Q_{2}/Q_{1} = (400)^{4} – (300)^{4}/ (500)^{4} – (300)^{4} = 0.32.
Two spheres A and B of same material have radius 1 m and 4 m, and temperatures 4000 K and 2000 K respectively. Then the energy radiated by sphere A is
E_{ A}/E_{ B} = (1)^{2} (4000)^{4}/ (4)^{2} (2000)^{4} = 1.
A small body has a total emissive power of 4.5 kW/m^{2}. Determine its surface temperature of maximum emission
E = σ T^{4}. So, T = 530.77 K.
A small black body has a total emissive power of 4.5 k W/m^{2}. In which range of the spectrum does this wavelength fall?
(Wavelength) T = 2.8908 * 10^{3}. This must be the wavelength of infrared region.
The sun emits maximum radiation of 0.52 micron meter. Assuming the sun to be a black body, Calculate the surface temperature of the sun
T = 2.8908 * 10^{ 3}/0.52 * 10 ^{6} = 5573 K.
Consider the previous problem, determine the maximum monochromatic emissive power of the sun’s surface
(E)_{ MAX }= 1.285 * 10^{5}T^{5} = 6.908 * 10^{13} W/m^{2}.
A furnace emits radiation at 2000 K. Treating it as a black body radiation, calculate the wavelength at which emission is maximum
(Wavelength) T = 2.8908 * 10^{ 3}. So, wavelength = 1.449 * 10^{ 6} m.
Four identical pieces of copper painted with different colors of paints were heated to the same temperature and then left in the environment to cool. Which of the following paint will give fast cooling?
The emissivity of black paint is highest i.e. unity. Consequently, the emitted radiant energy will be maximum when painted black.
A surface for which emissivity is constant at all temperatures and throughout the entire range of wavelength is called
Foe grey surface, emissivity is constant. Grey surface radiates much more because of constant wavelength throughout its entire surface.
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