Question

A black body, at a temperature of ${227}^{o}C$, radiates heat at a rate of $20$cal $m^{-2}{s}^{-1}$. When its temperature is raised to ${727}^{o}C$, the heat radiated by it in cal $m^{-2}{s}^{-1}$ will be closest to:

• A. $40$
• B. $160$
• C. $320$
• D. $640$

Answer 1

The correct option is C $320$

We know that
$E=\sigma T^4$ $\Rightarrow$ $\frac{E_1}{E_2}=\frac{T_1^4}{T_2^4}$
$\Rightarrow$ $\frac{E}{20}=\frac{{(727+273)}^4}{{(227+273)}^4}=\frac{{\left(1000\right)}^4}{{\left(500\right)}^4}$
$\frac{E_1}{20}={\left(\frac{2}{1}\right)}^4=\frac{16}{1}$
$\Rightarrow$ $E_1=20\times 16=320cal$ $m^{-2}{s}^{-1}$