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Work done by a Gas

  1. Dec 22, 2015 #1
    1. The problem statement, all variables and given/known data
    A 1.00 mol sample of an ideal diatomic gas at a pressure of 1.00 atm and temperature of 420 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.60 atm. Determine the work done by this gas during this process.

    2. Relevant equations
    PV = nRT and W = int(PdV)

    3. The attempt at a solution
    So, i checked online for a solution and checked the official solutions manual, after i was stumped for awhile. My biggest issue is that both agree that volume changes. But if P = nR/V *T, and P varies linearly with T, then how is V not a constant? Or if it is changing, then how is n still a constant?
     
  2. jcsd
  3. Dec 22, 2015 #2

    SammyS

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    It's a 1 mole sample. What does that tell you about n ?
     
  4. Dec 22, 2015 #3
    If n is constant, then how is V not constant? The slope of the straight line (in this case slope = nR/V) should be constant. If n and R are to be constants, then i assume that V should be constant as well. However, neither solution i have checked show this.
     
  5. Dec 22, 2015 #4

    SammyS

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    It must be that there is heat transfer involved as well.
     
  6. Dec 22, 2015 #5
    I am missing something. If heat is added, can the temperature still vary linearly with pressure? Or is it no longer an ideal gas.
     
  7. Dec 22, 2015 #6

    SammyS

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    That may have been a bit misleading.

    The statement says that P varies linearly with T. It does not say that they are proportional.
     
  8. Dec 22, 2015 #7
    So, there must be a nonzero y-intercept. Thanks, that clears it up!
     
  9. Dec 22, 2015 #8

    SammyS

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    Yes. That's the trick.
     
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