Question 346: Properties of Matter

Question

The power radiated by a black body is P and it
radiates maximum energy at wavelength, $\lambda $
0
. If
the temperature of the black body is now
changed so that it radiates maximum energy at
wavelength ${3 \over 4}{\lambda _0}$, the power radiated by it
becomes nP. The value of n is

Accepted Answer

From Wien's law, $\lambda $
max
T = constant
$ 	herefore $ $\lambda $
max
1
T
1
= $\lambda $
max
2
T
2
$ \Rightarrow $ $\lambda $
0
T
1
= ${{3{\lambda _0}} \over 4}$T
2
$ \Rightarrow $ ${{T_2} \over T_1} = {4 \over 3}$
According to Stefan-Boltzmann law, energy emitted
unit time by a black body is Ae$\sigma $T
4
,
$ 	herefore $ P $ \propto $ T
4
So ${{{P_2}} \over {{P_1}}} = {\left( {{{{T_2}} \over {{T_1}}}} ight)^4}$ = ${\left( {{4 \over 3}} ight)^4}$
Here, P
2
= nP and P
1
= P
So, ${{nP} \over P} = n = {\left( {{{{T_2}} \over {{T_1}}}} ight)^4} = {\left( {{4 \over 3}} ight)^4} = {{256} \over {81}}$

Answer

${3 \over 4}$

Answer

${4 \over 3}$

Answer

${{256} \over {81}}$

Answer

${{81} \over {256}}$

Properties of Matter

The power radiated by a black body is P and it radiates maximum energy at wavelength, \lambda 0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength {3 \over 4}{\lambda _0}, the power radiated by it becomes nP. The value of n is

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