Question

A black body radiates energy at the rate of $E$ watt $/ m ^{2}$ at a high temperature $T K$. When the temperature is reduced to $\left(\frac{T}{2}\right) K$, the radiant energy is

• A. $\frac{E}{2}$
• B. $2\, E$
• C. $\frac{E}{4}$
• D. $\frac{E}{16}$

Answer 1

Answer: (D)

According to Stefan's law,
$E \propto T^{4}$
or $\frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}$
or $\frac{E_{2}}{E}=\left(\frac{T / 2}{T}\right)^{4}=\left(\frac{1}{2}\right)^{4}$
or $E_{2}=\frac{E}{16}$