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Temperature

Call the rms ...

Question

Call the rms speed of the molecules in an ideal gas $v_{0}$ at temperature $T_{0}$ and pressure $P_{0}$ . Find the speed if the temperature is raised from $T_{0} = 293 K$ to $573 K$ .

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Solution

Since rms speed is related to temperature as

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

Thus, $v_{r m s} α \sqrt{T}$

Hence, $\frac{{v^{'}}_{r m s}}{v_{0}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{573}{293}} = 1.4$

Thus $v^{'} = 1.4 v_{0}$

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