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Maxwell's Speed of Distribution Law

Identify the ...

Question

Identify the correct order of temperature as indicated in given diagram for same gas.

T_{1} > T_{2} > T_{3}

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T_{3} > T_{2} > T_{1}

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T_{1} > T_{2} = T_{3}

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T_{1} = T_{2} > T_{3}

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Solution

The correct option is A $T_{1} > T_{2} > T_{3}$
We know that, the peak indicates the most probable speed.
$v_{m p} = \sqrt{\frac{2 R T}{M}}$
$\Rightarrow v_{m p} \propto T^{1 / 2}$
As temperature increases, $v_{m p}$ also increases.

From graph, it is clear that
$v_{m p 1} > v_{m p 2} > v_{m p 3} \Rightarrow T_{1} > T_{2} > T_{3}$
Therefore, correct order of temperature is $T_{1} > T_{2} > T_{3}$

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