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Finding Final temp for Adiabatic process

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data

    A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Assume the initial pressure and temperature of the air before it is put in the tire to be Pi = 1.00 bar and Tf 287K . The final pressure in the tire is Pf = 3.75 bar.

    Calculate the final temperature of the air in the tire. Assume that CV,m = 5R/2.
    2. Relevant equations
    dU=nCvmdt
    dU=dw...as q=0 adiabaitc
    dw=-Pexdv
    using these above equations my notes derive the following
    ViTic=VfTfc where c=Cvm/R
    PiVi[itex]\gamma[/itex]=PfVf[itex]\gamma[/itex] where gamma=Cpm/Cvm

    3. The attempt at a solution

    I am really stuck on where to even start this problem. It seems as if i am missing info, that i need a number of moles or a volume or something. I cant seem to find a way to rearange any of the above. In other problems it boiled down to using the boring old ideal gas pv=nrt to solve for one variable but again this leaves me with 2 unknows so im not sure what to do.

    Any tips, hints, explanations anything would be a great help!


    [itex]\gamma[/itex]
     
    Last edited: Oct 17, 2013
  2. jcsd
  3. Oct 17, 2013 #2
    can i say that So im thinking can i say that
    (Tf/Ti)^c=Vi/Vf and (Pf/Vf)^(1/gamma)=ViVf

    so that (Tf/Ti)^c=(Pf/Vf)^(1/gamma)


    is this legit?
     
  4. Oct 18, 2013 #3

    DrClaude

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    Staff: Mentor

    You have a couple of typos in there. Rewrite it more carefully.
     
  5. Oct 25, 2013 #4

    Andrew Mason

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    Science Advisor
    Homework Helper

    Try expressing the adiabatic condition in terms of T and P. Think of the air in the tire at the end as a compression of a much greater volume of air at atmospheric pressure into the final volume of the tire.

    AM
     
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