The adjoining diagram shows the spectral energy density distribution Eλ of a bl

Question

The adjoining diagram shows the spectral energy density distribution

E_{λ}

of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, find the value of temperature T.

Options:

A . 3000K

B . 4000 K

C . 5000 K

D . 6000 K

Answer: Option B
:
B
Area under curve represents the emissive power of the body

\frac{E_{T}}{E_{2000}} = \frac{A_{T}}{A_{2000}} = \frac{16}{1}

(given) ...(i)
But from Stefan's law E α T4

∴ \frac{E_{T}}{E_{2000}} = {(\frac{T}{2000})}^{4}

...(ii)
From (i) and (ii)

{(\frac{T}{2000})}^{4} = \frac{16}{1}

\Rightarrow \frac{T}{2000} = 2 \Rightarrow T = 4000 k

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