Question

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

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

Answer 1

The correct option is D $400\%$

According to Question

$T_2=T_1+\frac{50T_1}{100}$

$T_2=\frac{15T_1}{10}$

Percentage increases in radiation is

$\frac{E_2-E_1}{E_1}\times 100$

$\frac{{T_2}^4-{T_1}^4}{{T_1}^4}\times 100$

$\frac{{\frac{15T_1}{10}}^4-{T_1}^4}{{T_1}^4}\times 100$

$\frac{{15}^4-{10}^4}{{10}^4}\times 100$

$\frac{50625-10000}{10000}\times 100$

$\frac{40625}{100}$

$406.25\approx 400$

Option (D) is correct option