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Truck cylinder, ideal gas law problem

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    One cylinder in the diesel engine of a truck has an initial volume of 500 cm^3. Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 450 J of work to rapidly compress the air. What is its final temperature? What is its final volume?

    2. Relevant equations

    PV = nRT
    [tex]\Delta[/tex] Eth = (5/2)nR[tex]\Delta[/tex]T

    3. The attempt at a solution

    I found the temperature using the second equation to be 1100 C which is right. However i cannot find the final volume for the life of me. I tried P[tex]\gamma - 1[/tex]T-[tex]\gamma[/tex] and use the final pressure to find the volume but that didn't seem to work. Is there another way to go about this?
     
  2. jcsd
  3. Feb 24, 2009 #2
    finally figured it out using the formula:

    W = PV[tex]\gamma[/tex](Vf1-[tex]\gamma[/tex] - Vi1-[tex]\gamma[/tex])/(1 - [tex]\gamma[/tex])
     
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