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Molar specific heat of an ideal gas

  1. Nov 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A sample of a diatomic ideal gas has pressure P and volume V. When the gas is warmed, it's pressure triples and the it's volume doubles. This warming process includes two steps, the first at constant pressure and the second at constant volume. Determine the energy transferred by heat.


    2. Relevant equations

    Q = nCvΔT(constant volume)
    Q = nCpΔT(constant pressure)

    3. The attempt at a solution
    Since it occurs in two phases, my thought was to add Q1 + Q2. Q1 at constant pressure and Q2 at constant volume i.e.

    (n x 7/2R x ΔT) +(n x 5/2R x ΔT)
    nRΔT is common thus;
    nRΔT(7/2 + 5/2)
    = 6nRΔT. or 6PV (since PV = nRT)

    But my answer is wrong..and i'm NOT sure if my conclusion that nRΔT = nRT is true..
    Any help is very much appreciated..thanks
     
  2. jcsd
  3. Nov 10, 2011 #2

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    Hi fiziks09! :smile:

    Did you notice that you did not use the information that the pressure triples and the volume doubles?

    Consider also that you don't know ΔT of each process step. They will not be the same.
     
  4. Nov 10, 2011 #3
    thanks..
    i noticed that..but the thing is i don't know where to fit that information. I also can't think of any other equations relevant to the question aside from the ones in put up there
     
  5. Nov 10, 2011 #4

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    What about the ideal gas formula: PV=nRT?
     
  6. Nov 10, 2011 #5
    Okay..i have been on this quite a while now..
    i substituted n = PV/RT in the equations for both constant pressure and constant volume..
    i then used p = 3P and v = 2V.. but it didn't work..

    Also..how about the initial states of the gas, i couldn't figure out where to fit them in ?.
     
  7. Nov 10, 2011 #6

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    What did not work?

    The initial state of the gasses would be P=Po, and V=Vo.

    Step 1 is constant pressure, so V changes from Vo to 2Vo at P=Po.
    Furthermore Q = nCpΔT. Calculate ΔT from P and V.

    Step 2 is constant volume, so P changes from Po to 3Po at V=2Vo.
    Furthermore Q = nCvΔT. Calculate ΔT from P and V.
     
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