The graph, shown in the adjacent diagram, represents the variation of temperature $(T)$ 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 [2003]

Question

Smart Achievers · Accepted Answer

(3)

From the graph,

${(\frac{- d T}{d t})}_{x} > {(- \frac{d T}{d t})}_{y}$

Rate of cooling,

$(- \frac{d T}{d t}) \propto emissivity (e)$

$∴$ $E_{x} > E_{y}$

Also $a_{x} > a_{y}$ as good absorbers are good emitters.

Solution

Q.
The graph, shown in the adjacent diagram, represents the variation of temperature $(T)$ 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 [2003]

1 $E_{x} > E_{y} & a_{x} < a_{y}$

2 $E_{x} < E_{y} & a_{x} > a_{y}$

3 $E_{x} > E_{y} & a_{x} > a_{y}$

4 $E_{x} < E_{y} & a_{x} < a_{y}$

Ans.
(3)

From the graph,

${(\frac{- d T}{d t})}_{x} > {(- \frac{d T}{d t})}_{y}$

Rate of cooling,

$(- \frac{d T}{d t}) \propto emissivity (e)$

$∴$ $E_{x} > E_{y}$

Also $a_{x} > a_{y}$ as good absorbers are good emitters.

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Solution

Q. The graph, shown in the adjacent diagram, represents the variation of temperature (T) 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 [2003]

1 Ex>Ey & ax<ay

2 Ex<Ey & ax>ay

3 Ex>Ey & ax>ay

4 Ex<Ey & ax<ay

Ans. (3) From the graph, (-dTdt)x>(-dTdt)y Rate of cooling, (-dTdt)∝emissivity (e) ∴ Ex>Ey Also ax>ay as good absorbers are good emitters.