The graph shown in the adjacent diagram represents the variation of temperature (.T.) of two bodies x and y having the same surface area, with time ( t ). Both of these bodies lose heat only due to the emission of radiation. Find the correct relation between the emissive and absorptive power of the two bodies.

Question

The graph shown in the adjacent diagram represents the variation of temperature (.T.) of two bodies x and y having the same surface area, with time ( t ). Both of these bodies lose heat only due to the emission of radiation. Find the correct relation between the emissive and absorptive power of the two bodies. Question

(A) Ex>Ey and ax < ay (B) Ex < Ey and ax>ay (C) Ex>Ey and ax>ay (D) Ex < Ey and ax < ay

Tardigrade Admin · Accepted Answer

Rate of cooling (- (dT/dt)) propto emissivity (e) From the graph, (- (dT/dt))x>(- (dT/dt))y ∴ ex>ey Further emissivity ( e ) propto absorptive power ( a ) (good absorbers are good emitters also) ∴ ax>ay

$E_{x} > E_{y} an d a_{x} < a_{y}$

$E_{x} < E_{y} an d a_{x} > a_{y}$

$E_{x} > E_{y} an d a_{x} > a_{y}$

$E_{x} < E_{y} an d a_{x} < a_{y}$

Rate of cooling $(- \frac{d T}{d t}) \propto$ emissivity $(e)$
From the graph,
$(- \frac{d T}{d t})_{x} > (- \frac{d T}{d t})_{y}$
$∴$ $e_{x} > e_{y}$
Further emissivity ( $e$ ) $\propto$ absorptive power ( $a$ ) (good absorbers are good emitters also)
$∴$ $a_{x} > a_{y}$

Ex​>Ey​andax​<ay​

Ex​<Ey​andax​>ay​

Ex​>Ey​andax​>ay​

Ex​<Ey​andax​<ay​

Rate of cooling (−dtdT​)∝ emissivity (e) From the graph, (−dtdT​)x​>(−dtdT​)y​ ∴ ex​>ey​ Further emissivity ( e ) ∝ absorptive power ( a ) (good absorbers are good emitters also) ∴ ax​>ay​

$E_{x} > E_{y} an d a_{x} < a_{y}$

$E_{x} < E_{y} an d a_{x} > a_{y}$

$E_{x} > E_{y} an d a_{x} > a_{y}$

$E_{x} < E_{y} an d a_{x} < a_{y}$

Rate of cooling $(- \frac{d T}{d t}) \propto$ emissivity $(e)$
From the graph,
$(- \frac{d T}{d t})_{x} > (- \frac{d T}{d t})_{y}$
$∴$ $e_{x} > e_{y}$
Further emissivity ( $e$ ) $\propto$ absorptive power ( $a$ ) (good absorbers are good emitters also)
$∴$ $a_{x} > a_{y}$