Question

Light bulb 1 operates with a filament temperature of 2600 K, whereas light bulb 2 has a filament temperature of 1900 K. Both filaments have the same emissivity, and both bulbs radiate the same power. Find the ratio A1/A2 of the filament areas of the bulbs.

Answer 1

The radiance accoridng to Stefan Boltzmann law is

$I=\sigma T^4$

and the power is

$P=AI$

Thus, recalling power are teh same for both filaments

$A_1\sigma T_1^4=A_2\sigma T_2^4$

$\frac{A_1}{A_2}=\frac{T_2^4}{T_1^4}=3.5$