Question

The rate of emission of radiation of a black body at temperature ${37}^o$C is E. If its temperature is increased to ${347}^o$C, then the rate of emission of radiation will be.

• A. $4$E
• B. $16$E
• C. $2$E
• D. $32$E

Answer 1

Answer: (B)

$16$E

From Stefan's law, we have
$E=\sigma T^4$
$\therefore E\propto T^4$
$\therefore \frac{E_1}{E_2}={\left(\frac{T_1}{T_2}\right)}^4$
$\Rightarrow \frac{E}{E^{\prime }}={\left(\frac{37+273}{347+273}\right)}^4={\left(\frac{310}{620}\right)}^4$
$={\left(\frac{1}{2}\right)}^4=\frac{1}{16}$
$\therefore E^{\prime }=16E$.