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Maxwell's Distribution of Speeds

If the absolu...

Question

If the absolute temperature of a gas in a fixed volume is quadrupled, then the velocity in initial and final states would be related as

A

v_{f} = 4 v_{i}

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B

v_{f} = v_{i} / 4

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C

v_{f} = v_{i} / 2

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D

v_{f} = 2 v_{i}

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Solution

The correct option is B $v_{f} = 2 v_{i}$
If the absolute temperature of a gas in a fixed volume is quadrupled, then the velocity in initial and final states would be related as $v_{f} = 2 v_{i}$
Velocity is directly proportional to the square root of temperature.
$v \propto \sqrt{T}$
$\frac{v_{f}}{v_{i}} = \sqrt{\frac{T_{f}}{T_{i}}}$
$\frac{v_{f}}{v_{i}} = \sqrt{\frac{4 T_{i}}{T_{i}}}$
$\frac{v_{f}}{v_{i}} = \sqrt{4}$
$\frac{v_{f}}{v_{i}} = 2$
$v_{f} = 2 v_{i}$ .
Thus, the option (D) is the correct answer.

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