First slide

Radiation

Question

The thermal emissivities of two bodies A and B are in the ratio of $\frac{1}{e}$ . The outer surface area of the bodies are same and they radiate energy at the same rate. Find the ratio of the wavelengths corresponding to the maximum spectral radiancy in the radiation from A to maximum spectral radiancy in the radiation from B:

Moderate

A

$e^{\frac{1}{4}}$
B

$\frac{1}{e^{\frac{1}{4}}}$
C

${(1 + e)}^{\frac{1}{4}}$
D

$\frac{1}{{(1 + e)}^{\frac{1}{4}}}$

Solution

P = $1 \times {AσT}_{A}^{4} = {eAσT}_{B}^{4}$
$T_{A} = e^{\frac{1}{4}} T_{B}$
   $λ_{A} T_{A} = λ_{B} T_{B}$
or    $e^{\frac{1}{λ}} λ_{A} T_{B} = λ_{B} T_{B}$
   $\frac{λ_{A}}{λ_{B}} = \frac{T_{B}}{e^{\frac{1}{4}} T_{B}} = \frac{1}{e^{\frac{1}{4}}}$

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