Question

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

• A. 0.054
• B. 0.0034
• C. 1
• D. 2

Answer 1

Answer: (A)

Total energy radiated from a body
$ Q=A{{\varepsilon }_{0}}{{T}^{4}}t $
$ \Rightarrow $ $ Q\propto A{{T}^{4}}\propto {{r}^{2}}{{T}^{4}} $
$ (\because A=4\pi {{r}^{2}}) $
$ \therefore $ $ \frac{{{Q}_{p}}}{{{Q}_{Q}}}={{\left( \frac{{{r}_{p}}}{{{r}_{Q}}} \right)}^{2}}{{\left( \frac{{{T}_{p}}}{{{T}_{Q}}} \right)}^{4}} $
$ ={{\left( \frac{8}{2} \right)}^{2}}{{\left( \frac{273+127}{273+527} \right)}^{4}}=1 $