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Q.

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $λ_{0}$ . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{5} λ_{0}$ , the power radiated by it becomes $n P$ . The value of $n$ is :-

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a

$\frac{3}{5}$

b

$\frac{4}{3}$

c

$\frac{625}{81}$

d

$\frac{81}{625}$

answer is C.

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Detailed Solution

$P = σ A T^{4} \Rightarrow P \propto T^{4} λ_{m_{1}} T_{1} = λ_{m_{2}} T_{2} \Rightarrow λ_{0} T = \frac{3}{5} λ_{0} T_{2} \Rightarrow T_{2} = \frac{5}{3} T ∴ P_{2} = C \times {(\frac{5}{3} T)}^{4} = \frac{625}{81} \times P ∴ n = \frac{625}{81}$

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The power radiated by a black body is P and it radiates maximum energy at wavelength λ0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 35λ0 , the power radiated by it becomes nP. The value of n is :-