The graph, shown in the diagram, represents the variation of temperature (T) of the 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}

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

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

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

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Solution

The correct option is C $E_{x} > E_{y} a n d a_{x} > a_{y}$
Rate of cooling $(- \frac{d T}{d t}) \infty$ emissivity (e)
From the graph,
${(- \frac{d T}{d t})}_{x} > {(- \frac{d T}{d t})}_{y}$
$∴ E_{x} > E_{y}$
Further emissivity (E) = absorptive power (a) (good absorbers are good emitters also)
$∴ a_{x} > a_{y}$

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