Two spherical black bodies of radii R1 and R2 and with surface temperature T1 and T2 respectively radiate the same power. R1/R2 must be equal to

Q: Two spherical black bodies of radii R₁ and R₂ and with surface temperature T₁ and T₂ respectively radiate the same power. R₁/R₂ must be equal to

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

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

(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 $