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Identify process in a heat engine

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm taking a practice test and I need some help with a heat engine problem.
    There are three parts, the one that's giving me trouble is a-->b. The Volume v. Pressure graph shows a straight line. Pa= 5 atm Va= 5 L Ta=300K and Tb=800K are given.
    So pressure is decreaseing, while volume and temperature are increasing. What type of process is this? How could I find Pb or Vb?

    2. Relevant equations

    For an adiabatic process:
    PaVa^(5/3)=PbVb^(5/3)=constant
    TaVa^(2/3)=TbVb^(2/3)=constant
    W=-dU(internal energy)=-(3/2)RTln(Vb/Va)

    3. The attempt at a solution
    I initially thought this was adiabatic expansion but that cannot be true because of the temperature increase (as far as my limited knowledge can tell). All my calculations yield nonsense answers so I really do not think it could be adiabatic; but I may be wrong of course. Other than that I have no idea
     
  2. jcsd
  3. Mar 18, 2013 #2
    In an adiabatic process, temperature DO change: the adiabatic process is the one in which there is no heat exchange with the outside, but temperature will change.

    This said, you're right, it can't be an adiabatic process anyway, because i) if pressure decreases and volume increases, then temperature would decrease in an adiabatic process, and also ii) it is not represented with a straight line, but with a curve...

    A straight line with both pressure and volume increasing sounds as no elementary transformation to me (it is neither an isochoric transf. nor an isobaric one). Also isothermal would have constant temperature so nothing to do. The only chance I see is to use a composite transformation. You could try seeing if you can connect the starting and arriving point with an isothermal and an adiabatic transformation, but the simplest way should be to use an isochoric and an isobaric.

    In practice you can try to reach the final pressure with constant volume and then leave the same pressure and vary volume to reach also final volume. This is the only way I can think of anyway.
     
  4. Mar 18, 2013 #3

    DrClaude

    User Avatar

    Staff: Mentor

    Can you use the information of b-->c to figure out the conditions at b?
     
  5. Mar 18, 2013 #4
    I found that Pa= 10Pc so I was able to find Vc and b-->c is isovolumetric so Vc=Vb. The only question remaining is what type of process could this be?!
    Thank you all for your replies. It's not isobaric/choric because both pressure and volume are changing. I'm glad you all agree that it can't be adiabatic. Maybe a-->b isn't a process that has any sort of special characteristics other than the ideal gas law. I should be able to find W and Q from other equations.
     
  6. Mar 18, 2013 #5
    I am not aware of any special name for a transformation which is not isobaric/choric and is straight at the same time... then it has to be a general transformation for a perfect gas, and that's all
     
  7. Mar 18, 2013 #6
    I think you're right Tia. I used W=PdV and dU=Q-W to find W and Q. Thanks for your help!
     
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