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A thermodynamics problem

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://img101.imageshack.us/img101/7498/thermo.jpg [Broken]

    A cylinder is closed by a massless piston of cross sectional area A which is connected to a spring of constant k. With the spring relaxed, the cylinder is filled with a gas. The initial pressure, volume and temperature are Pi Vi and Ti. How high will the piston rise if its temperature is increased to a final value of Tf?

    2. Relevant equations

    3. The attempt at a solution

    I tried to find Pf and Vf.

    Pf = Pi + kx/A
    Vf = Vi + Ax

    I then wrote the universal gas law for Pf Tf and Vf but I doubt this is correct because the equation was crazy long and complicated.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 3, 2010 #2

    ehild

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    In spite of being crazy long ad complicated, it might be correct. There were no numerical data?

    ehild
     
  4. Aug 3, 2010 #3
    Nope, only letters. Are the expressions I wrote for Pf and Vf correct?
     
  5. Aug 3, 2010 #4

    Andrew Mason

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    You have written out the expression for the pressure as a function of x and volume as a function of x. All you have to do is relate that, using the ideal gas law, to the change in temperature.

    AM
     
  6. Aug 3, 2010 #5

    ehild

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    I think they are correct. But the expression for x will be really ugly. Just go ahead.

    ehild
     
  7. Aug 3, 2010 #6
    That gives a quadratic equation:

    kx2 + (PiA + kVf/A)x + nR(Ti-Tf) = 0

    I highly doubt this is the correct answer because this is an old exam question and impossible to do in ~10 minutes.
     
  8. Aug 3, 2010 #7

    ehild

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    Well, it is not quite correct, there should be Vi instead of Vf in your term kVf/A. And you should replace nR by piVi/Ti.

    Then use the formula for the solution of quadratic equations and exclude the negative root. It takes less time than 20 s.

    ehild
     
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