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 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 :
Updated On: Sep 7, 2025
- 450
- 1000
- 1800
- 225
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The Correct Option is C
Solution and Explanation
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
$r \propto R^{2} T^{4}$
$\frac{r_{1}}{r_{2}}=\frac{R_{1}^{2} T_{1}^{4}}{R_{2}^{2} T_{2}^{4}}$
$=4 \times \frac{1}{16}$
$\frac{450}{r_{2}}=\frac{1}{4}$
$r_{2}=1800$ watt
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