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Homework Help: Adiabatic compression of an ideal gas

  1. Apr 16, 2007 #1
    An ideal gas at a temperature of 17.7°C is compressed adiabatically from an initial volume 70.0 l to a final volume 43.0 l. Find its final temperature (in °C) if CV = 2.50R.

    so T1V1^g=T2V2^g

    to find g=cp/cv=(cv+nR)/cv and cv=2.50R

    g=(2.50R+nR)/2.50R factor out an R g=(2.50+n)/2.50 factor out 2.50


    but how do i find n....if what i did above is even right
  2. jcsd
  3. Apr 16, 2007 #2

    Andrew Mason

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    It helps to start with the correct relationship. The adiabatic condition is:

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

    Substitute P = nRT/V to give:

    [tex]TV^{\gamma-1} = K/nR = constant[/tex]

    You can't determine what n is since you don't have the pressure. But you don't need it to solve the question.

    Last edited: Apr 16, 2007
  4. Apr 16, 2007 #3
    so how do i get what i denoted as g
  5. Apr 16, 2007 #4
    do i solve for what ever nR is
  6. Apr 16, 2007 #5
    i am so confused! please give me another hint
  7. Apr 16, 2007 #6

    Andrew Mason

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    What is [itex]TV^{\gamma-1}[/itex] initially?

    Does it change?

    So what is it at the end?

    You are given the volume at the end. So what is T at the end?

    Note: [itex]\gamma = C_p/C_v \text{ and } C_p = C_v + R[/itex]

    [itex]\gamma[/itex] is simply a ratio of specific heats so it is dimensionless.

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