Question

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

• A. $185\%$
• B. $285\%$
• C. $325\%$
• D. $130\%$

Answer 1

The correct option is A $185\%$

According to Stefan's law,amount of radiations emitted
$E\propto T^4$,

$\frac{E^{\prime }}{E}=\frac{{[T+\left(\frac{30}{100}\right)T]}^4}{T^4}$

$={\left[\frac{130}{100}\right]}^4$

$=(1.3{)}^4$

The percentage increase in $E$ is given as:

$=\frac{E^{\prime }-E}{E}\times 100$

$=(\frac{E^{\prime }}{E}-1)\times 100$

$=\left(\right(1.3{)}^4-1)100\%=185\%$