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Definition of Relations

Two spheres P...

Question

Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures $127^{0}$ C and $527^{0}$ C respectively. The ratio of energy radiated by P and Q is

0.054

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0.0034

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Solution

The correct option is C
1

$T o t a l e n e r g y r a d i a t e d f r o m a b o d y Q = A ϵ σ T^{4} t \Rightarrow Q α A T^{4} α r^{2} T^{4} (∵ A = 4 π r^{2}) \Rightarrow \frac{Q_{p}}{Q_{Q}} = {(\frac{r_{p}}{r_{Q}})}^{2} {(\frac{T_{p}}{T_{Q}})}^{4} = {(\frac{8}{2})}^{2} {\frac{(273 + 127)}{(273 + 527)}}^{4} = 1$

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