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!

Determining pressure in Interstellar space

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H2). The number density is about 1atom / cm3 and the temperature is about 3 K. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.

    2. Relevant equations
    Average translational kinetic energy per molecule: Eavg = 1.5KbT = .5mv2
    p = F/A = (1/3)(N/V)mVrms2
    Eth = 1.5nRT
    pV = nRT

    3. The attempt at a solution
    V = 10-6 m3
    T = 3K
    m = 1u = 1.66x10-27
    n = 1.66x10-24 (not sure if this is right?)

    pV = nRT --> p = 4.14x10-17
    Where am I going wrong, or is this correct?

    Thank you for any help/advice!
  2. jcsd
  3. Sep 18, 2011 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Different approach, I get the same number:

    \frac{10^6 \, \text{atom}} {\text{m}^3} \cdot
    \frac{1 \, \text{mole}} {6.0221415 \times 10^{23} \, \text{atom}} \cdot
    8.3144621 \, \text{J}/\text{K}/\text{mole} \cdot
    3 \, \mbox{K} \approx 4.142 \times 10^{-17} \, \text{pascal}
  4. Sep 18, 2011 #3
    The only formula you need is PV = nRT
  5. Sep 18, 2011 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    That is exactly one of the formulae that pdonovan, Spinnor.
  6. Sep 18, 2011 #5
    Thank you very much, that was the correct answer.

    Now, how would I got about finding Vrms?

    I know p = (1/3)(N/V)mVrms2
    So, p = 4.14x10-17
    N = 1
    V = 10-6
    m = 1u = 1.66x10-27
    And found Vrms = .86m/s, but this is incorrect. I think my m or v might be incorrect.
  7. Sep 18, 2011 #6

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Your value for m is correct (assuming units of kilograms; always carry units around). Your math is wrong somewhere. Show your work.
  8. Sep 18, 2011 #7
    Now I have...

    4.14x10-17pa = (1/3)(1/10-6)mVrms2

    1.242x10-22 = mVrms2

    74819.28 = Vrms2
    Vrms = 275.64m/s

    So something is definitely wrong, because the atom should be moving very slowly.
  9. Sep 18, 2011 #8

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Yeah, your answer is too large. About 2 m/s too large. sqrt(74819.28) is about 273.53.

    As a sanity check, you can always compute sqrt((3 * boltzmann's constant * 3 kelvin) / (1 amu)). You will get the same answer.
  10. Sep 18, 2011 #9
    Then which values are wrong in the Vrms = sqrt(3KbT / m) formula? I have T = 3 and if m = 1, then Vrms = 1.11 x 10 ^ -11 which is wrong. And if m =1660x10^-27g it is too big (around 8.6).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Determining pressure in Interstellar space