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
B
25681P
C
1681P
D
72981P

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

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