1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating the root mean square speed from pressure and density.

  1. Jan 7, 2014 #1
    1. The problem statement, all variables and given/known data

    A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m-3, find the root mean square speed of the molecules.

    2. Relevant equations

    These are the equations I believe to be relevant:

    [tex]c_{rms} = \frac{\sqrt{<c^2>}}{N}[/tex]

    [tex]pV = \frac{1}{3}Nm<c^2>[/tex]

    [tex]p = \frac{1}{3}ρ<c^2>[/tex]

    3. The attempt at a solution

    [tex]\frac{3p}{ρ} = <c^2>[/tex]
    [tex]\frac{3 * 150000}{2} = <c^2> = 225000ms^{-1}[/tex]

    But I'm not sure how to work out N as I don't any volume or temperature. I'm not quite sure how they get their answer in the back of the book which is 474 ms-1 (which is the square root of 225000) meaning that N = 1? How can that be?

    Thank you for reading!
     
    Last edited: Jan 7, 2014
  2. jcsd
  3. Jan 7, 2014 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    If c^2 = 225000, then the units can't be m/s
     
  4. Jan 8, 2014 #3
    Sorry yes <c^2> should be in m^2s^-2 shouldn't it?
     
  5. Jan 8, 2014 #4

    BruceW

    User Avatar
    Homework Helper

    Are you sure there should be an ##N## here?
     
  6. Jan 8, 2014 #5
    I'm sure, atleast that's how they have quoted it in my text book:

    WEareEe.jpg
     
  7. Jan 8, 2014 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    How does your book define <c^2>?

    ehild
     
  8. Jan 8, 2014 #7
    It defines it as:

    [tex]<c^2> = \frac{{c_1}^2 + {c_2}^2 + {c_3}^2 + ....{c_N}^2}{N} = \frac{{c_i}^2}{N} [/tex]

    I'm not exactly sure what the right-hand most part means with the subscript i.
     
  9. Jan 8, 2014 #8

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It should be

    [tex]<c^2> = \frac{{c_1}^2 + {c_2}^2 + {c_3}^2 + ....{c_N}^2}{N} =\frac{\sum{{c_i}^2}}{N} [/tex]

    i is the summation index, and √<c2> itself is the rms speed. No need to divide it by N. [tex]\frac{3p}{ρ} = <c^2>[/tex]

    ehild
     
  10. Jan 8, 2014 #9

    BruceW

    User Avatar
    Homework Helper

    yeah, I think what ehild said is right. The equation
    [tex]c_{rms} = \frac{\sqrt{<c^2>}}{N}[/tex]
    is most likely a mistake in the book. It doesn't make sense, if you think about it. If you had a bunch of atoms all moving at the same speed, then this equation would give an rms value that is smaller for a larger population of these identical atoms. Which doesn't make sense at all.
     
  11. Jan 8, 2014 #10

    Okay, I've got it now, thanks for the explanation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculating the root mean square speed from pressure and density.
  1. Root mean square speed (Replies: 10)

Loading...