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Homework Help: Question on adiabatic expansion

  1. Dec 8, 2003 #1
    I've been struggling with this problem for an hour or so now, and can't seem to find the right answer. Perhaps someone here can help? I would be very grateful. ;)

    Two moles of an ideal gas ( = 1.40) expands slowly and adiabatically from a pressure of 5.09 atm and a volume of 12.7 L to a final volume of 30.0 L.

    I had to find this stuff first, and I know I have all of it right.

    final pressure: 1.528
    initial temp: 393.5K
    final temp: 279

    Find Q, W, dEint.

    I know Q is 0, and I know that Work and change in internal Energy are the opposite of eachother, but I can't seem to find the right value for them. I thought work = nRdT, which in this case is:

    2*.08214*(393.5-279)=1902.9

    However, that answer is wrong according to webassign. There is also a problem in my text book that is the same, except with different numbers, and i tried that one and got it wrong too. Anyone know what I'm doing wrong? Your help is greatly appreciated. :)
     
  2. jcsd
  3. Dec 8, 2003 #2
    Formula for work done in adiabatic process is wrong
     
  4. Dec 8, 2003 #3
    so what is the proper formula? The textbook goes through a proof of why PV^y is constanst, but doesn't really go any further from that... I'm guessing that's somehow incorperated into the formula...
     
  5. Dec 8, 2003 #4
    Write the differential equation for for work done for gas
    i.e
    dW=PdV

    Note [tex]PV^\gamma= K[/tex]

    substitute P from above in workdone equation and calculate the work done by taking limits from V1 to v2
     
  6. Dec 8, 2003 #5
    eh... P from above what? P is not constant.
     
  7. Dec 8, 2003 #6
    Refining it
    [tex] dW=kV^-^\gamma dV [/tex]

    I hope u will got it now
     
    Last edited: Dec 8, 2003
  8. Dec 8, 2003 #7
    Okay, I thought maybe that's what you meant, but I'm sorry I don't see what good that does if I don't know what k is. Maybe I'm just slow tonight as I only got about 4 hours of sleep last night and am rather tired... Sorry. [zz)]

    Ah well, it was due at midnight. So I'll just ask my teacher how to do it tomorrow...
     
    Last edited: Dec 8, 2003
  9. Dec 8, 2003 #8
    k is a constant which is given by

    [tex]PV^\gamma= k[/tex]

    [tex] P_iV_i^\gamma = P_fV_f^\gamma= k[/tex]
     
    Last edited: Dec 8, 2003
  10. Dec 10, 2003 #9
    Oh duh. Sorry, I guess I was just really tired last night. ;) Anyway thanks for the help.
     
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