Question

Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures ${127}^{o}C$ and ${527}^{o}C$ respectively. The ratio of energy radiated by P and Q is

• A. 0.054
• B. 0.0034
• C. 1
• D. 2

Answer 1

The correct option is C

1

Total energy radiated from a body $Q=Aϵ\sigma T^{4}t$
$\Rightarrow Q\propto A{T}^4\propto r^2{T}^4(\because A=4\pi r^2)$
$\Rightarrow \frac{Q_P}{Q_Q}=(\frac{r_P}{r_Q}{)}^2(\frac{T_P}{T_Q}{)}^4=(\frac{8}{2}{)}^2{\frac{(273+127)}{(273+527)}}^4=1$