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Physics-

General

Easy

Question

The adjoining diagram shows the spectral energy density distribution $E subscript lambda end subscript$ 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

$32,000 K$
$16,000 K$
$8,000 K$
$4,000 K$

The correct answer is: $4000 blank K$

$fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals fraction numerator 16 over denominator 1 end fraction$ [Given]
Area under $e subscript lambda end subscript minus lambda$ curve represents the emissive power of body and emissive power $proportional to T to the power of 4 end exponent$
$rightwards double arrow fraction numerator A subscript T end subscript over denominator A subscript 2000 end subscript end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow fraction numerator 16 over denominator 1 end fraction equals open parentheses fraction numerator T over denominator 2000 end fraction close parentheses to the power of 4 end exponent rightwards double arrow T equals 4000 K$

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