Question

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

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

Answer 1

The correct option is B $22$%

According to Stefan's law, the 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.

$T^{\prime }=T+\frac{5}{100}T=\frac{21}{20}T$

$\therefore \frac{H\prime }{H}={\left(\frac{T\prime }{T}\right)}^4={\left(\frac{21}{20}\right)}^4={\left(1.05\right)}^4$

% increase in the rate of heat energy

$\frac{H\prime -H}{H}\times 100=[{\left(1.05\right)}^4-1]\times 100\approx 22$