Power radiated by a block body at temperature $T_{1}$ is P and it radiates maximum energy at a wavelength $λ_{1}$ . If the temperature of the black body is changed from $T_{1}$ to $T_{2}$ , it radiates maximum energy at a wavelength $\frac{λ_{1}}{2}$ . The power radiated at $T_{2}$ is

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16P

answer is D.

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Detailed Solution

$(\frac{Q}{A t}) = σ T^{4}$

$P = A σ T^{4}$

$P \propto T^{4}$

$\frac{P_{1}}{P_{2}} = {(\frac{T_{1}}{T_{2}})}^{4} \to (1)$

But, $λ_{m_{1}} T_{1} = λ_{m_{2}} T_{2}$

$λ_{1} \times T_{1} = \frac{λ_{1}}{2} T_{2}$

$T_{2} = 2 T_{1}$

$\frac{P}{P_{2}} = {(\frac{T_{1}}{2 T_{1}})}^{4}$

$P_{2} = 16 P$

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