First slide

Radiation

Question

The rate of cooling at 600 K is H, if surrounding temperature is 300 K is H. The rate of cooling at 900 K is

Moderate

A

$\frac{16}{3} H$
B

2H
C

3H
D

$\frac{2}{3} H$

Solution

By Stefan's law, Rate of cooling, H $\propto (T^{4} - {T_{0}}^{4})$
$∴ \frac{H^{'}}{H} = \frac{{(900)}^{4} - {(300)}^{4}}{{(600)}^{4} - {(300)}^{4}} = \frac{9^{4} - 3^{4}}{6^{4} - 3^{4}} = \frac{3^{4} (3^{4} - 1)}{3^{4} (2^{4} - 1)}$
$∴ H^{'} = \frac{16}{3} H$

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