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Thermo: Need help finding T2 and V2 in an adiabat

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

    1 mole of ideal gas initially at 294 K is compressed adiabatically and
    reversibly from 0.83 atm to 10.0 atm. Calculate the initial and …final volumes,
    the final temperature, [itex]\Delta[/itex]U; [itex]\Delta[/itex]H; Q; and W: Assume that Cv = (5/2)R

    Given:

    n = 1 mol
    T1 = 294 K
    P1 = 0.83 atm
    P2 = 10 atm
    Q = 0

    Find
    V1, V2, [itex]\Delta[/itex]U, Q, [itex]\Delta[/itex]H, T2, W

    2. Relevant equations

    1. The professor gave that specific heat at constant volume is (5/2)R, however, the volume of the problem changes. Is this equation completely irrelevant to the problem?

    2. How to you find the final temperature and final volume?


    3. The attempt at a solution

    I started off with PV = nRT for the initial givens and obtained that V1 = 29.1 L

    Now, I'm stuck. I've tried using the ideal gas equation again, but I have 2 unknowns. I tried rearranging the equation and setting it equal the initial equations. I know how to find the other unknowns, but I'm stuck at this part for some reason.
     
  2. jcsd
  3. Sep 1, 2012 #2

    Andrew Mason

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    You need to use the adiabatic condition: [itex]PV^\gamma = constant = K[/itex] which can be rewritten: [itex]TV^{\gamma-1} = K/nR = constant[/itex]

    AM
     
  4. Sep 1, 2012 #3
    I'm assuming that the constant K will remain the same for p1*v1 and p2*v2

    If I set P1V1γ = K, then I can use that constant for P2V2γ and obtain the volume, correct?
     
  5. Sep 1, 2012 #4

    Andrew Mason

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    If it didn't, it would not be constant!

    Exactly.

    AM
     
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