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’s 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.

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

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

% increases in rate of heat energy$= \frac{H` - H}{H} \times 100$

$= \lbrack(1.05)^{4} - 1\rbrack \times 100$

$= 22\%$