Rms speed of ideal gas

  • Thread starter map7s
  • Start date
  • #1
146
0

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

  • #2
Doc Al
Mentor
45,084
1,394
Could it be a trick question? :wink:
 
  • #3
146
0
how would it be a trick question?
 
  • #4
rsk
241
133
Is anything changing? Is temperature changing? Have you given us the full question? If everything else is unchanged, then so is rms speed.
 
  • #5
Doc Al
Mentor
45,084
1,394
And that's why I'd call it a trick question. Be sure you state the problem completely, just in case.
 
  • #6
146
0
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.
 
  • #7
146
0
My mistake...it says that volume and pressure are constant but it says nothing about temperature.
 
  • #8
marcusl
Science Advisor
Gold Member
2,763
413
I'd say 1800 * sqrt(Tfinal / Tinitial)
 
  • #9
146
0
the only problem is that the temperature is not given
 
  • #10
146
0
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.
 
  • #11
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
7,051
18
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?
 
  • #12
146
0
...it would have to be a constant too, right?
 
  • #13
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
7,051
18
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
 
  • #14
146
0
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.
 
  • #15
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
7,051
18
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.
 
Last edited:

Related Threads on Rms speed of ideal gas

Replies
3
Views
2K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
0
Views
370
  • Last Post
Replies
0
Views
410
Replies
1
Views
19K
  • Last Post
Replies
0
Views
4K
Replies
1
Views
583
  • Last Post
Replies
6
Views
321
Replies
1
Views
3K
  • Last Post
Replies
5
Views
18K
Top