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Thermodynamics- total kinetic energy and rms velocity

  1. May 28, 2011 #1
    Find total kinetic energy and root mean square velocity of the molecules of 10 liters of helium gas at an equilibrium pressure of 105 N m−2. Density of helium is 0.1786 gram/liter.

    I am having trouble with the question, I know:


    PV=(Nm <v^2>)/3

    but I am not sure how to apply this.

    Any help would be appreciated.
  2. jcsd
  3. May 28, 2011 #2

    Andrew Mason

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    Can you find the temperature? What is the relationship between temperature and kinetic energy?

  4. May 29, 2011 #3
    I have partial solutions from my tutorial but they are not making too much sense...

    From the above equations, it goes:

    K= 1/2 Nm <v>^2 so if divide each side by V
    K= 1/2 ρ V <v>^2

    from here the solution goes:

    PV=1/3 Nm <v>^2

    K=3/2 PV I can see that 2K=3PV

    but i do not understand where the following equations come from:

    K=1/3 ρ V <v>^2 because this is what i need to rearrange to find Vrms.
  5. May 29, 2011 #4

    Andrew Mason

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    You did not answer my questions.

  6. May 29, 2011 #5
    I know that as the temp increases so does the kinetic energy.

    1/2 m <v>^2 = 3/2 KT
  7. May 29, 2011 #6

    Andrew Mason

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    You haven't answered my first question: what is the temperature of the Helium? (hint: assume it is an ideal gas).

  8. Jul 13, 2011 #7
    I'm not sure if you still need help with this question, but I'll show how I'd work it out:

    Firstly, to find the RMS (root mean squared) velocity of the molecules, we'll start with your equation,

    PV=(Nm <v^2>)/3 Now we don't know N, and while we could calculate it, its easier to rearrange this equation to form,
    P = (Nm<v^2>)/3V (multiplying both sides by V)
    P = (1/3)p<v^2> (using Nm/V = p (density) )

    Now we know p the density, and P the pressure so rearrange
    <v^2> = 3P/p
    <v^2> = 3 x 105 / (0.1786 x 10^-3 / 10^-3 ) [ensuring p is in kg/m^3]
    <v^2> = 1763.7178...
    RMS = 42.0 ms^-1 (3sf) [square root the <v^2>]

    Secondly to find the total Kinetic energy

    Start with what we have, so P = Nm<v^2> / 3V
    and K= 1/2 Nm <v^2>

    So 3PV = Nm<v^2>
    3PV/2 = 1/2 Nm<v^2>
    and since K = 1/2 Nm<v^2>
    We can state that K = 3/2 PV and can now substitute your values in to find the answer.

    There are many ways of solving these as they are all rearrangements of the same equation.
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