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Question

Total radiation power emitted by a black body is $$P$$ and it radiates maximum spectral intensity around wavelength $$\lambda$$. If the temperature of black body is changed so that now it emits maximum spectral intensity around wavelength $$\dfrac{3}{4} \lambda$$. Find the new power radiated by the body. 


A
19681P
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B
25681P
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C
1681P
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D
72981P
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Solution

The correct option is C $$\dfrac{256}{81}P$$
radition power $$\frac{E}{t}=eA\sigma T^4$$
$$\Rightarrow \boxed { \propto T^4}$$ 
For maximum spectral intensity relation 
$$\lambda T=constant{ <Weins Law}$$
$$\lambda_1T_1=\lambda_2T_2$$
given that 
$$\lambda _1=\lambda $$
$$\lambda_2=\frac{3\lambda}{4}$$
$$\boxed{\frac{T_2}{T_1}=\frac{\lambda_1 }{\lambda _1}=\frac{4}{3}}$$

Power    $$\frac{P_1}{P_2}=\frac{T_1}{T_2}^4\Rightarrow  P_2 =P_1 (\frac{T_2}{T_1})^4=P(\frac{4}{3})^4$$
$$\boxed {P_2=P\times \frac{256}{81}}$$

1184522_145534_ans_4cc82714e83d4bae910c3a415ff5fdf8.jpg

Physics

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