Question

If the temperature of hot black body is raised by $5\%$, rate of heat energy radiated would be increased by how much percentage ?

• A. $12\%$
• B. $22\%$
• C. $32\%$
• D. $42\%$

Answer 1

Answer: (B)

$22\%$

Answer 2

According to Stefan?? law, rate of energy radiated by a black body at absolute temperature $T$ is given by $H=A\sigma T^{4}$ where $A$ is the area of the emitting surface. $T'=T+\frac{5}{100}T=\frac{21}{20}T$ $\therefore \frac{H'}{H}=\left(\frac{T'}{T}\right)^{4}$ $=\left(\frac{21}{20}\right)^{4}=\left(1.05\right)^{4}$ $\%$ increase in rate of heat energy $=\frac{H'-H}{H}\times 100$ $=\left[\left(1.05\right)^{4}-1\right]\times 100\approx 22\%$