Question

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

• A. $185\%$
• B. $285\%$
• C. $325\%$
• D. $130\%$
• E. 245%

Answer 1

Answer: (A)

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