Question

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

• A. 225
• B. 450
• C. 900
• D. 1800

Answer 1

The correct option is D 1800

We know that radiation from the body is given as $E=ϵ\sigma A{T}^4$
$\frac{E_1}{E_2}=\frac{r_1^2{\times T}_1^4}{r_2^2{\times T}_2^4}=\frac{{0.12}^2{\times 500}^4}{{0.06}^2\times {1000}^4}$
$E_2=\frac{450\times {0.06}^2\times {1000}^4}{{0.12}^2\times {500}^4}=1800watt$