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Homework Help: Adiabatic process - Diesel engine

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    A diesel engine requires no spark plug. The air in a cylinder is compressed so
    highly that the fuel spontaneously ignites when sprayed into cylinder. If the air is
    initially at 20°C and is then compressed by a factor of 15 in volume, what final
    temperature is attained (before fuel injection)? Assume the compression is adiabatic,
    and treat the air as an ideal gas. Take delta = 1.4 for air. By what factor does the
    pressure increase?

    2. Relevant equations
    PV^ delta = constant
    TV ^delta-1 = constant.
    Delta = Cp/Cv.

    Internal energy = Work done.
    3. The attempt at a solution

    I am totally lost with this problem, I know what an adiabatic process is, how to derive the delta, etc but I can't seem to match that with the above question.

    Any tips ?
    Last edited: Oct 15, 2011
  2. jcsd
  3. Oct 16, 2011 #2
    I think I have got an idea...
    We know TV^delta -1 = constant...
    Could I use the following relation :
    T1 V1 ^delta -1 = T2 V2 ^delta-1

    To get my t2 value?

    No that doesn't seem right...

    How about this :
    T[itex]V^{\gamma-1}[/itex] = k.

    So if I plug in my initial temperature value as : 293.15 k and volume assumed to be at 1 , that will give me a value = k.

    For the final temperature:
    [itex]T_{2}[/itex][itex]V^{\gamma-1}[/itex] = k
    so t2 * (1/15)^ 1.4-1 = 5863/20
    which gives me t2 = 866k.

    =] ?
    Last edited: Oct 16, 2011
  4. Oct 16, 2011 #3
    Your answer is correct. Assume isentropic so exponent is specific heat ration. Your equation is:

    T2/T1 = (V1/v2)^(k-1)

    You know the volume ratio, T1, and you know k.
  5. Oct 16, 2011 #4
    thanks you very much! : ))))))))))))))))))))))))))))))
  6. Oct 16, 2011 #5
    Also at the end of the question it asks by how much factor has hte pressure risen.. which according to my calculations is ~ 44 times.

    Is this correct too ?
  7. Oct 16, 2011 #6
    Yes, that is what I get for two significant figures.
  8. Oct 16, 2011 #7
    Thanks for your help! :))
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