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Heat engine cycles

  1. Nov 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Taken from adkins Introduction to thermal physics

    A reversible heat engine is operated between two bodies, one
    of heat capacity C1 initially at temperature T1 and the other of
    heat capacity C2 initially at temperature T2. As the engine
    operates, the warmer body gradually cools and the cooler one
    is warmed.
    (a) By considering the changes that occur in one cycle of the
    engine, show that infinitesimal changes of temperature of the
    two bodies are related by

    0 = C1 dT1/T1 + C2 dT2/T2

    Eventually, the bodies reach the same temperature Tf and
    the heat engine ceases to run. Show that Tf is given by

    TfC1 + C2 = T1C1 T2C2

    2. Relevant equations

    U = Q + W

    3. The attempt at a solution

    For the first part

    I am taking the U to be 0 and W = 0 ... This probaly is not be correct.

    0 = C1 (T1 + dt) + C2(T2-dt)... this does lead me to the correct solution.

    Any hints would be greatly appreciated!
     
    Last edited: Nov 1, 2012
  2. jcsd
  3. Nov 1, 2012 #2
    Alright I figured out this question ...

    Its a simple manipulation of the dQ = T ds equation for each Temperature. Then you can equate them by using S1 = -S2 and finally integrate.

    The last part of this question ask what the Tf would be if the process was irreversible. I think this would just be the average:

    Tf = (T1 + T2)/2

    however I have a feeling I am missing something. Any suggestions would be great!
     
    Last edited: Nov 1, 2012
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