Q. 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%
Explanation
(d) $Q \propto T^{4} \Rightarrow \frac{Q_{1}}{Q_{2}} = \left( \frac{T_{1}}{T_{2}} \right)^{4}$
$\Rightarrow \frac{Q_{1}}{Q_{2}} = \left( \frac{T}{T + T/2} \right)^{4} = \frac{16}{81} \Rightarrow Q_{2} = \frac{81}{16}Q_{1}$
% increase in energy $= \frac{Q_{2} - Q_{1}}{Q_{1}} \times 100 = 400\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.