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Non-Quasistatic Compression

  1. Oct 1, 2013 #1
    1. The problem statement, all variables and given/known data

    A cylinder contains one liter of air and room temperature (300 K) and atmospheric pressure (105 N/m2). At one end of the cylinder is a massless piston, whose surface area is 0.01m2. Suppose that you push the piston in VERY suddenly, exerting 2000N. The piston moves only one millimeter before it is stopped by an immovable barrier of some sort.

    a) How much work have you done on this system?
    b) How much heat has been added to the gas?
    c) Assuming that all the energy added goes into the gas (not the piston or cylinder walls), by how much does the internal energy of the gas increase?
    d) Use the thermodynamic identity to calculate the change in the entropy of the gas (once it has again reached equilibrium.

    2. Relevant equations

    dW = -P dV
    Q = T dS (quasistatic)
    dS > Q/T when W > -P dV --> in text for example problem much like this.
    dU = T dS - P dV (thermodynamic identity)
    ΔU = Q + W

    3. The attempt at a solution
    My big issue right now is that the equations presented in the chapter for this scenario are > / < not =, therefore, how can I know how much work and heat go into the system??
    Without that, I just go through the numbers as usual with W = P * dV = 2000 N / 0.01 m2 * (0.001 m) * (0.01 m2), which gives me a solid number.
    Then I believe this process is adiabatic, therefore, the Q = 0
    Which then makes c) really easy since it's just work going into the system.
    d) then becomes a simply math problem.
    Is this right? Is the problem supposed to be this simple?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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