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Thermodynamics: box with a moving wall

  1. Dec 7, 2017 #1
    • Moved from a technical forum, so homework template missing
    I have a doubt regarding the answer, a box separated by a movable wall has two compartments filled by a monotonic gas .Initially the volumes are equal but the pressure are 3P and P respectively .When the wall is allowed to move the final pressure is
    a.(2/3)γP
    b.3(2/3)γP
    C.(1+31/γ)γP/2
    D.(31/γ/1+31/γ)γP
    I have a doubt regarding option c as in the denominator I m getting 2ϒ
    I want to clarify whether I m right
     
  2. jcsd
  3. Dec 7, 2017 #2
    I think you are right, I also obtain 2γ.
     
  4. Dec 7, 2017 #3

    DrClaude

    User Avatar

    Staff: Mentor

    Please show your work.
     
  5. Dec 7, 2017 #4
    3PVϒ=pV1ϒ
    PVϒ=pV2ϒ
    and V1+V2=2V
    Where p=final state pressure and V1 and V2 are final state volume of the two boxes,V is the initial state volume
    Solving the above three the result comes
     
  6. Dec 7, 2017 #5
    The equations you are attempting to use are valid strictly to the case of an adiabatic reversible expansion and/or compression. If the wall is allowed to move with no constraint, the process will not be reversible, and the equations will not apply. Only if, during the process, the motion of the wall is controlled externally in very gradual increments will it be possible to carry out the process reversibly.

    What is the exact statement of the problem?
     
  7. Dec 7, 2017 #6
    the four options are given and only one is right,using the arguments given previous I obtained option c with an amendment I want to clarify whether I have done right and what will be the correct option
     
  8. Dec 7, 2017 #7
    What is the EXACT statement of the problem?
     
  9. Dec 7, 2017 #8
    Is the wall force to move gradually (so that the volume changes of the gases are reversible) or is it allowed to move freely (unconstrained)? Is the wall insulated (so that no heat can flow from one side to the other), or is it conductive of heat?
     
  10. Dec 7, 2017 #9
    it is allowed to move freely and the wall is insulated
     
  11. Dec 7, 2017 #10
    If this is the case, then none of the answers is correct.
     
  12. Dec 7, 2017 #11
    ok thank you
     
  13. Dec 7, 2017 #12
    If the wall is forced to move gradually (not freely) and the wall is insulated, then the correct answer is C, if the 2 in the denominator is corrected to be ##2^{\gamma}##. If the wall is allowed to move freely and is not insulated, the final pressure is 2P.

    It is also possible to approximate the solution to this problem if the wall is insulated and allowed to move freely if we assume that, on both sides of the wall, the pressure throughout the process is constant and equal to the final value of the pressure.
     
  14. Dec 7, 2017 #13
    thanks it helps me in clearing the concept
     
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