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1st Law of Thermo, work in a piston.

  1. Aug 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Air is expanded in a piston-cylinder arrangement at a constant P of 200kPa from a volume of 0.1 m3 to a volume of 0.3m3. Then the temperature is held constant during an expansion to a volume of 0.5m3. Predict the total work done in the air.


    2. Relevant equations
    W = ∫PdV , PV = nRT


    3. The attempt at a solution
    For the first part of the expansion I used:
    W = ∫PdV = P∫dV = P(V2 - V1) = 200,000Pa ( 0.3-0.1)m3
    and got W = 40,000J.

    The next expansion is what is confusing me.
    Since Pressure is no longer constant I need to leave it in the W = ∫PdV equation.
    So, I transform this equation using the ideal gas eqn. PV = nRT and get:
    W = nRT∫dV/V = nRT*ln(V3/V2)
    But, without knowing the n or the T how do I get the work?

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 29, 2012 #2

    TSny

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    Trick: Replace the nRT in your expression for W with some other expression (using the ideal gas law).
     
  4. Aug 29, 2012 #3
    Since Temperature is constant for this part I can assume P2V2=P3V3 and find P3 and then replace nRT in my work equation with P3V3 (PV = nRT).
    After my computations I got 30,649.54J which sounds within reason.

    Was this what you were thinking?
     
  5. Aug 29, 2012 #4

    TSny

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    Yes. But there's no need to find P3. You can use P2 and V2 instead of P3 and V3.
     
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