Question

If the average velocity of the molecules of a gas is doubled, then what will happen to the root mean square velocity?

Answer 1

When $v_{avg}$ is doubled $v_{rms}$ will also be doubled .

We know , average velocity and  root mean square velocity is given by :

$v_{avg}=\sqrt{\dfrac{8RT}{\pi M}}$ and $v_{rms}=\sqrt{\dfrac{2RT}{M}}$

It is also given that both the gas are same. Therefore , M is constant .

Here we can see that both of these two quantities depends on only absolute temperature.

Therefore , when $v_{avg}$ is doubled $v_{rms}$ will also be doubled .

Hence , this is the required solution .

Learn More in the topic thermodynamics .

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Answer 2

Given:

Final average velocity of molecules of gas = 2 × Initial average velocity of molecules of gas.

To Find:

The final root mean square velocity of the molecules of the gas.

Calculation:

- We have:

Initial V(av) = √8RT/πM

Initial V(rms) = √3RT/M

⇒ V(rms)/V(av)  = √(3RT/M)/√(8RT/πM)

⇒ Initial V(rms) = √(3π/8) × V(av)  

- It is given that Final V(av) = 2 × Initial V(av)

⇒Final V(rms) = √(3π/8) × 2 × Initial V(av)

⇒Final V(rms) =  2 × Initial V(rms)

- So if we double average velocity, then the root mean square velocity also gets doubled.