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Ideal gas - monatomic or diatomic?

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data

    5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ.

    Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure C sub c,m and at C sub v,m

    2. Relevant equations
    PV = nRT
    C = dQ/dT
    Cp = Cv + nR
    Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas

    3. The attempt at a solution
    No idea where to start... help please!
     
  2. jcsd
  3. Jan 15, 2012 #2

    I like Serena

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    Hi shyguy79! :smile:

    In a constant pressure process you have Cp=dQ/dT.
    Can you calculate Cp from that?
    What would you get if you divide Cp by nR?
     
  4. Jan 15, 2012 #3
    Where dQ = 29.1x10^3 and dT = 200K then Cp = 145.5 J K^-1

    Is nR = 5 x 8.314 = 41.57 ???? but why would you do this?

    so Cp/nr = 3.5 ???? How does this relate?
     
  5. Jan 15, 2012 #4

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    Yep. That is correct.

    What would Cp/nR be for a monatomic gas?
    And for a diatomic gas?
     
  6. Jan 15, 2012 #5
    Cp = (f/2 +1) nR so then Cp/nR = (f/2 +1)

    so for a monatomic gas... 3/2 + 1 = 2.5
    for a diatomic gas... 5/2 +1 = 3.5

    so the gas is diatomic?
     
  7. Jan 15, 2012 #6

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    Right. :)
     
  8. Jan 15, 2012 #7
    Thank you so much! I've been stuck on this for ages!
     
  9. Jan 15, 2012 #8
    Just one question though what equation would be referenced for dividing Cp by nR?
     
  10. Jan 15, 2012 #9

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    Not sure what you mean...?

    You've used 3 of your relevant equations and solved for "f".
     
  11. Jan 15, 2012 #10
    doh! Yeah, just noticed - thanks again!
     
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