Q: Two spherical black bodies of radii R_{1} and R_{2} and with surface temperature T_{1} and T_{2} respectively radiate the same power. R_{1}/R_{2} must be equal to

(a) $\large (\frac{T_1}{T_2})^2$

(b) $\large (\frac{T_2}{T_1})^2$

(c) $\large (\frac{T_1}{T_2})^4 $

(d) $\large (\frac{T_2}{T_1})^4 $

Ans: (b)

Sol: $\large E = e \sigma A T^4 $

$\large E = e \sigma (4 \pi R^2) T^4 = constant $

$\large R_1^2 T_1^4 = R_2^2 T_2^4 $

$\large \frac{R_1}{R_2} = (\frac{T_2}{T_1})^2 $