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  4. The temperature of a radiating body increases by 30 %. Then the increase in the amount of radiation is

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Q. The temperature of a radiating body increases by $30\%$. Then the increase in the amount of radiation is

KEAMKEAM 2009Thermal Properties of Matter

Solution:

According to Stefan’s law, amount of radiations emitted
$E \propto T^{4}$,
$\therefore \frac{E'}{E}=\frac{\left[T+\left(\frac{30}{100}\right)T\right]^{4}}{T^{4}}$
$=\left[\frac{130}{100}\right]^{4}=\left(1.3\right)^{4}$
Percentage increase in $E$
$=\frac{E'-E}{E} \times 100$
$=\left(\frac{E'}{E}-1\right) \times 100$
$=\left(\left(1.3\right)^{4}-1\right)100$
$=185\%$