Question

Two bulbs have filaments of lengths, emmisivities and diameters in the ratio of 2:1 .If ratio of their powers is 1:2 then,ratio of their temperatures is

Answer 1

use the formula,

$P=e\sigma AT^4$

where e is emissivity, $\sigma$ is Stefan-Boltzmann's constant , A is cross sectional area and T is temperature.

here, two bulbs have filaments of lengths, emmisivities and diameters in the ratio of 2:1 .also the ratio of their powers is 1:2.

i.e., $\frac{P_1}{P_2}=\frac{e_1A_1T_1^4}{e_2A_2T_2^4}$

$\frac{P_1}{P_2}=\frac{e_1}{e_2}\frac{\pi \frac{d_1^2}{4}}{\pi\frac{d_2^2}{4}}\left(\frac{T_1}{T_2}\right)^4$

or, 1/2 = (2/1) × (2/1)² × $\left(\frac{T_1}{T_2}\right)^4$

or, 1/2⁴ = $\left(\frac{T_1}{T_2}\right)^4$

or, $\frac{1}{2}=\frac{T_1}{T_2}$

hence, ratio of their temperatures is 1 : 2.