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Homework Help: Piston with string

  1. May 26, 2010 #1
    1. The problem statement, all variables and given/known data
    A cylinder is equipped with a smoothly movable piston which is connected by a spring to the bottom of the cylinder as shown in the figure. An ideal gas of 0.1 mol is confined in the space on the left side of the cylinder at a temperature of 300 K. The atmospheric pressure is 1 x 105 Pa. Take the cross-section area of the piston to be 1 x 10-3 m2, the spring constant to be 500 N/m and the gas constant to be 8.3 J / mol K

    untitled-4.jpg

    1. Initially the spring is at its natural length. Calculate the volume of the gas

    By heating the gas, the piston moves to the right a distance of 0.2 m
    2. Calculate the pressure of the gas after the change

    3. Calculate the temperature of the gas after the change

    4. Calculate the work done by the gas during the change


    2. Relevant equations
    W = p ΔV
    PV / T = constant
    F = kx
    W = 1/2 kx2



    3. The attempt at a solution

    1. done (ans = 2.5 x 10-3 m3 )

    2.
    P = F/A = kx/A = (500) (0.2)/(1 x 10-3) = 1 x 105 Pa

    but the answer is 2 x 105 Pa.

    So should it be the initial pressure + P = 1 x 105 Pa + 1 x 105 Pa = 2 x 105 Pa ??

    3. no problem if (2) done

    4. work done = 1/2 kx2 = 1/2 (500) (0.2)2 = 10 J

    but the answer is 30 J...don't know what to do and why I was wrong...

    thanks
     
  2. jcsd
  3. May 26, 2010 #2
    The piston/ cylinder is exists at room temperature. Inside the cylinder the pressure is a 1 X 10^ 5 pa creating a force of 100N on the piston. Outside the cylinder is the same pressure and force so everything is in equilibrium. You heat the gas in the cylinder the spring compresses and pushes back with 100 N. So the total force on the outside face of the cylinder is 200N, Total force inside the cylinder is 200n or 2 X 10^5 pa. This 200 N force moves the piston .2 m doing 40J of work but the spring does 10J of work in the opposite direction, 40J-10J = 30 J total work done.
     
  4. May 26, 2010 #3
    wew, didn't cross my mind before...thanks a lot !!
     
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