Q: Two bodies A and B having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by A and B are in the ratio

(a) 1 : 1.15

(b) 1 : 2

(c) 1 : 4

(d) 1 : 16

Ans: (a)

Sol: $\large E \propto T^4 $

$\large \frac{E_1}{E_2} = (\frac{T_1}{T_2})^4$

$\large \frac{E_1}{E_2} = (\frac{273+10}{273 +20})^4$

$\large \frac{E_1}{E_2} = (\frac{283}{293})^4 = (\frac{293-10}{293})^4$

$\large \frac{E_1}{E_2} = (1- \frac{10}{293})^4 = 1- \frac{40}{293}$

$\large \frac{E_1}{E_2} = \frac{253}{293} = \frac{1}{293/253} $

$\large \frac{E_1}{E_2} = \frac{1}{1.15} $