# Rms speed of ideal gas

## Homework Statement

An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. If the initial rms speed is 1800 m/s, what is the final rms speed?

## Homework Equations

v(rms)=square root of [v(avg)]^2=square root of (3kT)/m

## The Attempt at a Solution

This was the only equation that I could find that dealt with rms speed, but the only problem is that I'm not sure how I can use just the initial rms speed to solve for the final rms speed with this equation.

## Answers and Replies

Doc Al
Mentor
Could it be a trick question? how would it be a trick question?

Is anything changing? Is temperature changing? Have you given us the full question? If everything else is unchanged, then so is rms speed.

Doc Al
Mentor
And that's why I'd call it a trick question. Be sure you state the problem completely, just in case.

I understand what you're saying now. The problem says that temperature and pressure are kept constant and to find the final rms speed. I tried entering in the same speed as the answer, but the program said that that was the wrong answer.

My mistake...it says that volume and pressure are constant but it says nothing about temperature.

marcusl
Science Advisor
Gold Member
I'd say 1800 * sqrt(Tfinal / Tinitial)

the only problem is that the temperature is not given

I sent my teacher an e-mail and he said, "First form the ratio of V_rms(ini)/V_rms(final), then you will see that
to find the ratio of the rms speeds what you need is the ratio of the
temperatures, which you can find using PV = NkT = constant" but I'm not sure how to figure out T w/o any values.

Gokul43201
Staff Emeritus
Science Advisor
Gold Member
I sent my teacher an e-mail and he said, "First form the ratio of V_rms(ini)/V_rms(final), then you will see that
to find the ratio of the rms speeds what you need is the ratio of the
temperatures, which you can find using PV = NkT = constant" but I'm not sure how to figure out T w/o any values.
If PV = NkT and all of P, V, N and k are constant, then what can you say about T?

...it would have to be a constant too, right?

Gokul43201
Staff Emeritus
Science Advisor
Gold Member
Yes, it would.

In general, as long as the gas is in a closed container (no molecules can enter or escape, so N is fixed), you can rewrite the above equation as:

(P1V1)/(P2V2) = T1/T2

In this case, if P1=P2 and V1=V2, that leaves you with T1/T2=1

so if I set it up as a ratio, like my teacher said, then it would be v(rms,i)/v(rms,f)=T1/T2=1
so v(rms,i)/v(rms,f)=1
so v(rms,i)=v(rms,f) right?
But that would mean that they would equal each other and I already plugged in that number and the program said that it wasn't correct.

Gokul43201
Staff Emeritus
Science Advisor
Gold Member
Either the program has it wrong, or you didn't write down the question correctly, or there's a typo in the question. Can't really say which it is.

Maybe the best you can do is take the above (corrected - see PS below) argument to your teacher, and find out where the problem is.

PS: There's a square root you're missing. v2/v1 = sqrt(T2/T1) - look at the equation you wrote down in the opening post.

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