First slide

Radiation

Question

The rectangular surface of area 8cm x 4cmof a black body at a temperature of $127^{0}$ C emits energy at the rate of E per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to $327^{0}$ C, the rate of emission of energy will become:

Moderate

A

$\frac{3 E}{8}$
B

$\frac{81}{16} E$
C

$\frac{9}{16} E$
D

$\frac{81}{64} E$

Solution

$\frac{Q}{t} \propto A T^{4}$
$\frac{Q_{1}}{Q_{2}} = \frac{A_{1}}{A_{2}} \frac{T_{1}^{4}}{T_{2}^{4}} = \frac{A}{\frac{A}{4}} {(\frac{400}{600})}^{4}$
$\frac{E}{Q_{2}} = 4 (\frac{16}{81})$
$Q_{2} = \frac{81 E}{64}$

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