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Ideal gas law in terms of density

  1. May 15, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-5-15_2-14-24.png

    2. Relevant equations
    PV=nRT

    3. The attempt at a solution
    not sure if this is the right approach

    upload_2015-5-15_2-17-38.png

    plugging into -ρg gives us -PMg/RT = dP/dy

    now we have to integrate both sides to find P?
     

    Attached Files:

  2. jcsd
  3. May 15, 2015 #2
    How you can write n as?
     
  4. May 15, 2015 #3
    n? number of moles?
     
  5. May 15, 2015 #4
    Yes
     
  6. May 15, 2015 #5
    n = mass/molecular mass
     
  7. May 15, 2015 #6
    The approach is right. What do you get if you integrate?
     
  8. May 15, 2015 #7
    well, i have no idea how to integrate that! :(

    i only know how to integrate stuff like x2 + 3
     
  9. May 15, 2015 #8
    No, problem.
    Do you know differentiation?
     
  10. May 15, 2015 #9
    no, i'm suppose to take that next year :(
     
  11. May 15, 2015 #10
    Oh, okay
    Then for the moment remember
    $$ \int dx/x = lnx + C $$
    Now use this in your problem.
    And tell what you are getting.
     
  12. May 15, 2015 #11
    i'm staring at this and still have no idea what to do, ok, so I know i can take the constants out and put it behind the integral

    (-Mg/RT) ∫ P = dP/dy

    correct? all the constants are out except P
     
  13. May 15, 2015 #12
    Ah, you may also not know the definite integration. I may have to do lot of work here.
    $$ \frac{-Mg}{RT}\int_0^{8812} dy = \int_{10^5}^P \frac{dp}{P} $$
    At ground height is zero and pressure 105 pascals.
    At height 8812 m we have to find pressure. The limits are taken accordingly.
    Now I guess you know how to solve further ?
     
  14. May 15, 2015 #13
    the left side of the equation should equal -1.095, correct?
     
  15. May 15, 2015 #14
    I must go to school now, i will finish this problem next time.
     
  16. May 15, 2015 #15
    Yes, and what right side evaluates to?
     
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