Question

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

• A. 1800
• B. 900
• C. 3600
• D. 850

Answer 1

The correct option is A 1800

Power radiated P $=A\epsilon \sim T^4$
$P=\left(\pi r^2\right)\epsilon \sim T^4$ $[\because A=\pi r^2]$
$⟹P\propto r^2{T}^4$
$\frac{P_1}{P_2}={\left(\frac{r_1}{r_2}\right)}^2{\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{r}{r/2}\right)}^2{\left(\frac{T}{2T}\right)}^4=\frac{1}{4}$
$P_2=4\times P_1=4\times 450=1800W$