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Thermodynamics: Heat and Work in a Cylinder

  1. Sep 7, 2015 #1
    1. The problem statement, all variables and given/known data
    Quiz_2_Q4.jpg

    2. Relevant equations
    W = ∫pdV
    W = (1/2)*k*(x2212)
    F = p*A
    3. The attempt at a solution
    Quiz_2_Q4_Diagram.jpg
    Assumptions made:
    1. Quasistatic process.
    2. Pressure is constant.

    Force balance on the piston reveals
    -> = <-
    p0*Apiston = patm*Apiston hence p0 = patm = 101 kPa

    From states 1-2 this is a constant pressure process:

    W12 = p0*Apiston*d1 = (101 kPa)(44*10-4 m2)(0.075m) = 33.333 Joules

    From states 2-3 this is both a constant pressure process and a spring compression process (taken separately):

    W23 (const) = p0*Apiston*d2 = (101 kPa)(44*10-4 m2)(0.075m) = 33.333 Joules

    W23 (spring) = (1/2)*k*(x2212) = (1/2)*(9800 N/m)(0.075m)2 = 27.562 Joules

    Total work done from the initial to the final state is equal to the summation of the three works done above:

    Wtotal = W12 + W23(const) + W23 (spring)
    Wtotal = 33.333 + 33.333 + 27.562 = 94.228 Joules of work done.

    Is my approach to this question reasonable? If not what can I do to fix or look up where I've gone wrong?

    As always, every ones help is greatly appreciated.
     
  2. jcsd
  3. Sep 7, 2015 #2
    Looks good.
     
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