First slide

Radiation

Question

A perfect black body emits radiation at temperature T₁ K. If it is to radiate 16 times this power, its temperature T₂ will be

Easy

A

$T_{2} = 16 T_{1}$
B

$T_{2} = 8 T_{1}$
C

$T_{2} = 4 T_{1}$
D

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

Solution

$Q \propto T_{1}^{4} and 16 Q \propto T_{2}^{4} or 16 = (T_{2}^{4} / T_{1}^{4}) or 2^{4} = {(T_{2} / T_{1})}^{4} ∴ T_{2} = 2 T$

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