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Thermodynamics: Compression of an Adiabatic Gas

  1. Mar 21, 2017 #1
    1. The problem statement, all variables and given/known data
    Assume 1.500 mol of a monatomic ideal gas is compressed from 3.00 L to 1.00 L.

    a. If the initial and final temperature is 10.0 °C, what are the initial and final pressures (in atm)?

    b. How much work input (in kJ) is required if a reversible isothermal path at 10.0 °C is followed?

    c. How much work input (in kJ) is required if the compression is adiabatic rather than isothermal? Assume the initial temperature is 10.0 °C.

    2. Relevant equations
    PV=nRT
    w=-nRTln(vf/vi)
    U=q+w

    3. The attempt at a solution
    I got both a and b using the first two equations I listed. I got the inital pressure to be 11.6 atm and the final pressure to be 34.8 atm. For the second part I got the work to be 3.88 kJ.

    I'm stuck on the third part. I know adiabatic means that there no change in U, so q=-w but I don't know how that applies to the question.
     
  2. jcsd
  3. Mar 22, 2017 #2

    DrClaude

    User Avatar

    Staff: Mentor

    You're missing an equation for the energy U of an ideal gas. And adiabatic does not mean ΔU = 0, it means q = 0.
     
  4. Mar 22, 2017 #3
    So ΔU=-PΔV, where U=w

    But the problem isn't isobaric, so that equation wouldn't work. I can't seem to find another equation though...
     
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