The adjoining diagram shows the spectral energy density distribut… - Vidyadip

MCQ

The adjoining diagram shows the spectral energy density distribution ${E_\lambda }$of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$ , the value of temperature $T$ is ........ $K$

A
$32,000 $
B
$16,000 $
C
$8,000 $
✓
$4,000 $

✓

Answer

Correct option: D.

$4,000 $

d
(d) $\frac{{{A_T}}}{{{A_{2000}}}} = \frac{{16}}{1}$ (given)
Area under ${e_\lambda } - \lambda $ curve represents the emissive power of body and emissive power $ \propto {T^4}$
(Hence area under ${e_\lambda } - \lambda $ curve) $ \propto {T^4}$

==>$\frac{{AT}}{{{A_{2000}}}} = {\left( {\frac{T}{{2000}}} \right)^4}$

==> $\frac{{16}}{1} = {\left( {\frac{T}{{2000}}} \right)^4}$==> $T = 4000K.$

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