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. $130\%$

Answer 1

Answer: (A)

$185\%$

Answer 2

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