Question

A spherical black body of radius 12cm radiates 450W power of 500k. If the radius is halved and the temperature is doubled the power radiated in watts would be

• A. 225
• B. 440
• C. 900
• D. 1800

Answer 1

Answer: (D)

1800

As we know that for radiation heat transfer is given as $\frac{Q}{t}=P=\sigma A{T}^4$
where, $A_{sphere}=4\pi r^2$
so $P=\left(4\pi r^2\right)\sigma T^4$
so $P\propto r^2{T}^4$
$\frac{P_2}{P_1}=\frac{r_2^2}{r_1^2}\times \frac{T_2^4}{T_1^4}=\frac{1^2}{2^2}\times 2^4=4$
So, $P_2=4P_1=4\times 450=1800Watt$