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Bodies A and ...

Question

Bodies A and B have thermal emissivities of $0.01$ and $0.81$ respectively. The outer surface areas of the two bodies are same. The two bodies emit total radiant power at the same rate. Find the temperature of B if the temperature of A is $5802 K$ .

A

1634 K

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B

1734 K

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C

1934 K

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D

None of these

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Solution

The correct option is C $1934 K$
Applying the Stefan Boltzmann law,
$P = e_{A} σ A T_{A}^{4} = e_{B} σ A T_{B}^{4}$
$T_{B} = {(\frac{e_{A}}{e_{B}})}^{1 / 4} T_{A} = {(\frac{0.01}{0.81})}^{1 / 4} (5802)$
$T_{B} = \frac{5802}{3} = 1934 K$

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