Power radiated by a black body is P and it radiates maximum energy around wavelength λ_0 . If tempe

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10-2.Transmission of Heat

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The power radiated by a black body is $P$ and it radiates maximum energy around the wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy around wavelength $\frac{3}{4}\lambda_0$, the power radiated by it will increase by a factor of

A

$4/3$

B

$16/9$

C

$64/27$

D

$256/81$

Solution

$\lambda_{\max } \alpha \frac{1}{T} \quad \Rightarrow \lambda_{\max } T=$ constant

$\Rightarrow \lambda_{\max _{1}} T_{1}=\lambda_{\max _{2}} T_{2}$

$\Rightarrow \lambda_{o} T=\frac{3 \lambda_{o} T^{1}}{4}$

$\Rightarrow T^{1}=\frac{4}{3} T$

So, $\frac{P_{2}}{P_{1}}=\left(\frac{T^{1}}{T}\right)^{4}=\left(\frac{4}{3}\right)^{4}=\frac{256}{81}$

Standard 11

Physics

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