Question

The rate of radiation of a black body at $0^{\circ} C$ is $E J . s ^{-1}$. The rate of radiation of the black body at $273^{\circ} C$ will be

• A. $E J . s^{-1}$
• B. $4 E J \cdot s ^{-1}$
• C. $\frac{E}{2} J \cdot s ^{-1}$
• D. $16 E J \cdot s^{-1}$

Answer 1

Answer: (D)

Given, $T_{1}=0^{\circ} C =(0+273) K=273\, K$
$T_{2}=273^{\circ} C =(273+273) K=546\, K$
According to Stefan-Boltzmann's law, rate of radiation,
$E \propto T^{4}$
$\therefore \frac{E_{2}}{E_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{4}$
$=\left(\frac{546}{273}\right)^{4}=(2)^{4}=16$
$\Rightarrow E_{2}=16 E_{1}=16 E J_{s}^{-1}\left[\because E_{1}=E J_{s}^{-1}\right]$