Question

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

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

Answer 1

Answer: (D)

Given, $T_1=0^{\circ }C=(0+273)K=273K$
$T_2=273^{\circ }C=(273+273)K=546K$
According to Stefan-Boltzmann's law, rate of radiation,
$E\propto T^4$
$\therefore \frac{E_2}{E_1}={\left(\frac{T_2}{T_1}\right)}^4$
$={\left(\frac{546}{273}\right)}^4=(2{)}^4=16$
$\Rightarrow E_2=16E_1=16E{J}_s^{-1}\left[\because E_1=E{J}_s^{-1}\right]$