Question

Two spheres made of same material and surface emit maximum radiation coressponding to wavelengths Lambda and 2Lambda. What is the ratio kf their radii so that they emit equal amount of radiant energy per unit time

Answer 1

Answer:

Ratio of radius of two sphere is 1 : 4

Explanation:

As we know by Wein's law of radiation that maximum radiation intensity wavelength is inversely depends on its temperature

So here we have

$\frac{\lambda_1}{\lambda_2} = \frac{T_2}{T_1}$

now we have

$\lambda_1 = \lambda$

$\lambda_2 = 2\lambda$

so we have

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

now we know that both sphere is radiating heat at same rate

So we have

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

so we have

$4\pi r_1^2 T_1^4 = 4\pi r_2^2 T_2^4$

so we have

$\frac{r_1}{r_2} = \frac{T_2^2}{T_1^2}$

$\frac{r_1}{r_2} = (\frac{1}{2})^2$

$\frac{r_1}{r_2} = \frac{1}{4}$

#Learn

Topic : Thermal radiation

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