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Physics-

General

Easy

Question

The graph, shown in the adjacent diagram, represents the variation of temperature $left parenthesis T right parenthesis$ of two bodies, $x$ and $y$ having same surface area, with time ( $t$ ) due to the emission of radiation. Find the correct relation between the emissivity and absorptivity power of the two bodies.

$E_{x} > E_{y} a n d a_{x} < a_{y}$
$E_{x} < E_{x} a n d a_{x} > a_{y}$
$E_{x} > E_{x} a n d a_{x} > a_{y}$
$E_{x} < E_{x} a n d a_{x} < a_{y}$

The correct answer is: $E subscript x end subscript greater than E subscript x end subscript a n d a subscript x end subscript greater than a subscript y end subscript$

Rate of cooling $left parenthesis negative fraction numerator d T over denominator d t end fraction right parenthesis proportional to$ emissivity(e)
From the graph,
$open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript x end subscript greater than open parentheses negative fraction numerator d T over denominator d t end fraction close parentheses subscript y end subscript$
$therefore e subscript x end subscript greater than e subscript y end subscript$
Further emissivity ( $e$ ) $proportional to$ absorptive power ( $a$ ) (good absorbers are good emitters also)
$therefore a subscript x end subscript greater than a subscript y end subscript$

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