Is RMS speed dependent on pressure?

[phymath7]

TL;DR

One question appeared in my test.It asked that if pressure of two gases are increased to two times of the previous,then how much change would happen to the ratio of the r.m.s speed of the two gases keeping the temperature constant?

As it is clear from the formula for r.m.s speed ,it is only dependent of temperture for a particular gas,I think the answer should be "No change happens".But I wonder whether there is more insight to this.And is my assumption true?

 

[DrClaude]

TL;DR Summary: One question appeared in my test.It asked that if pressure of two gases are increased to two times of the previous,then how much change would happen to the ratio of the r.m.s speed of the two gases keeping the temperature constant?

As it is clear from the formula for r.m.s speed ,it is only dependent of temperture for a particular gas,I think the answer should be "No change happens".But I wonder whether there is more insight to this.And is my assumption true?

You are correct.

I think that the insight is that one could think adding pressure will affect the motion of the gas particles, and hence their speed. (A higher pressure will affect the motion in some way. Can you see what it is?)

 

[phymath7]

You are correct.

I think that the insight is that one could think adding pressure will affect the motion of the gas particles, and hence their speed. (A higher pressure will affect the motion in some way. Can you see what it is?)

So you are saying that a higher pressure will somehow affect the r.m.s speed?But I don't see how it happens right now.

 

[jbriggs444]

So you are saying that a higher pressure will somehow affect the r.m.s speed?But I don't see how it happens right now.

If temperature is not forced to remain constant then consider how you go about increasing the pressure of the gas. Do you, for instance, force a piston further into a cylinder?

 

[DrClaude]

So you are saying that a higher pressure will somehow affect the r.m.s speed?But I don't see how it happens right now.

No, it doesn't affect r.m.s. speed, as you noted yourself. But it does affect something else related to the motion of the molecules.

 

[Andrew Mason]

So you are saying that a higher pressure will somehow affect the r.m.s speed?But I don't see how it happens right now.

Just apply the first law: $\Delta U = Q+W$ where W is the work done on the gas and Q is the heat flow into the gas.

A higher pressure without a change in volume (W=0) can only be achieved by increasing temperature ($\Delta U>0$) by positive heat flow (Q>0). Higher T means higher molecular rms speed (higher average molecular translational KE).

A higher pressure with compression requires positive work to be done on the gas (W>0). So if it is done adiabatically (Q=0) $\Delta U>0$ which results in higher molecular rms speed.

The only way to increase pressure without increasing molecular rms speed ($\Delta U \le 0$) is to compress with $Q+W\le 0$ (ie. heat flow out of the gas is greater than or equal to the work done on the gas).

AM