Question

A metal rod at a temperature of ${145}^{o}C$, radiates energy at a rate of $17W$. If its temperature is increased to ${273}^{o}C$, then it will radiate at the rate of

• A. $49.6W$
• B. $17.5W$
• C. $50.3W$
• D. $67.5W$

Answer 1

The correct option is A $49.6W$

Given, initial temperature of metal rod $\left(T_1\right)={145}^{o}C=418K$
Rate of radiated energy $\left(E_1\right)=17W$
Final temperature $\left(T_2\right)={273}^{o}C=273+273=546K$
We know, from the Stefan's law, $E\propto T^4$
or $\frac{E_1}{E_2}={\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{418}{546}\right)}^4$
$\therefore \frac{E_1}{E_2}=0.343$
Therefore, final radiated eneryg, $E_2=\frac{E_1}{0.343}$
$=\frac{17}{0.343}=49.6W$