Question

If the temperature of a hot body is increased by 50% then the increase in the quantity of emitted heat radiation will be

• A. 125%
• B. 200%
• C. 300%
• D. 400%

Answer 1

Answer: (D)

let us assume initial Temperature $T_1=T$ then final will be

$T_2=\frac{50}{100}T+T=\frac{150}{100}T=\frac{15}{10}T$

energy radiated

$e_1=\sigma A{T}_1^4\left(1\right)$

$e_2=\sigma A{T}_2^4\left(2\right)$

$\%$ increase in radiation

$=\frac{e_2-e_1}{e_1}\times 100$

$=\frac{\sigma A{T}_2^4-\sigma A{T}_1^4}{\sigma A{T}_1^4}\times 100$

$\frac{{\left(\frac{15}{10}T\right)}^4-T^4}{T^4}\times 100$

$\frac{{15}^4-{10}^4}{{10}^4}\times {10}^2$

$\frac{50625-10000}{{10}^2}$

$=406.25$

$\approx 400\%$

Hence $\left(d\right)$ option is correct.