Q105 / 180 · NEET 2017 · Physics

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

A
$225$
B
$450$
C
$1000$
Correct answer
D
$1800$

Solution

By Stefan's law rate of heat radiation from a black body

= σ A T^{4}

\Rightarrow

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 w a t t

Hence, the correct answer is option: 'D'.

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