How Does Constant Pressure Affect the Final RMS Speed of an Ideal Gas?

[map7s]

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.

 

[Doc Al]

Could it be a trick question?

 

[map7s]

how would it be a trick question?

 

[rsk]

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]

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

 

[map7s]

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.

 

[map7s]

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

 

[marcusl]

I'd say 1800 * sqrt(Tfinal / Tinitial)

 

[map7s]

the only problem is that the temperature is not given

 

[map7s]

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]

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?

 

[map7s]

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

 

[Gokul43201]

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

 

[map7s]

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]

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.