Question 145: Thermodynamics & KTG

Question

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Accepted Answer

We know, for an ideal gas,
${V_{rms}} = \sqrt {{{3RT} \over M}} $
$ \Rightarrow {V_{ms}} = V_{rms}^2 = {{3RT} \over M}$
$ \Rightarrow {V_{ms}} \propto T$
$ \Rightarrow {V_{ms}} \propto T$
i.e. mean squared velocity is directly proportional to temperature.
$ \Rightarrow {V_{ms}} = {\left( {{{3R} \over M}} \right)^T}$
by comparing it with $y=mx$ (straight line)
Hence, option 3 is correct.
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Thermodynamics & KTG

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Choose the correct answer: