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Homework Help: Thermodynamics Work, Heat, First Law Question

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider two pistons of equal cross sectional area joined as illustrated in the
    following sketch (my rendition):
    • Each piston contains n moles of an ideal gas of specific heat cV=(3/2) R.
    • Each piston's base is fixed, so when the rod joining the piston moves one
    must expand for the other to compress.
    • Piston A is thermally isolated and is initially at a pressure PA0 and a
    temperature T0.
    • Piston B is held in thermal equilibrium with a bath at temperature T0 and
    is initially at pressure PB0, which is higher than the initial pressure in
    piston A.
    • Piston B is allowed to expand quasi‐statically (reversibly) until there is no
    more net force on the rod joining the pistons. Piston B is frictionless, so
    during the expansion Pex=PB.
    A. Derive an expression that relates the following dimensionless
    π =P0B/P0A ,τ =TfA/T0A

    2. Relevant equations

    Ideal Gas: PVm=RT, dW=-PdV=CvdT

    3. The attempt at a solution

    Since the pistons are connected, when the piston stops moving, the work done in A will be equal to the work done by B?
    -nRT0A/V0A = nRT0B/V0B
    How do I relate to pressure from here?
    Also tried using Heat Capacity:
    Wadiabatic = Cv(delta)T, which should equal the W of the reversible adiabatic B undergoes:
    =-PdV = -nRT/V dV
    Again, I can't see how to proceed.

    Thank you!
  2. jcsd
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