First slide

Radiation

Question

A black body radiated maximum energy around a particular wavelength at a given temperature. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength n time the original wavelength (n<1) then power radiate by it will increases by a factor of

Moderate

A

$\frac{1}{n^{2}}$
B

$n^{2}$
C

$\frac{1}{n^{4}}$
D

$n^{4}$

Solution

$λ_{0} T_{0} = b$
   $P = {CT}_{0}^{4}$

or    $λ_{1} T_{1} = b$ $\Rightarrow n λ_{0} T_{1} = λ_{0} T_{0}$
So,    $T_{1} = \frac{T_{o}}{n}$
   $P_{1}$ = ${CT}_{1}^{4} = C {(\frac{T_{o}}{n})}^{4} = \frac{P}{n^{4}}$

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