Question

A spherical black body with a radius of $12\,cm$ radiates $450\,watt$ power at $500\,K$. If the radius were halved and the temperature doubled, the power radiated in watt would be :

• A. 450
• B. 1000
• C. 1800
• D. 225

Answer 1

The Correct Option is C

Rate of power loss
$r \propto R^{2} T^{4}$
$\frac{r_{1}}{r_{2}}=\frac{R_{1}^{2} T_{1}^{4}}{R_{2}^{2} T_{2}^{4}}$
$=4 \times \frac{1}{16}$
$\frac{450}{r_{2}}=\frac{1}{4}$
$r_{2}=1800$ watt