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Homework Help: Ideal Gas Question.

  1. Nov 13, 2008 #1
    1. The problem statement, all variables and given/known data
    1) Consider one-mole of gas in a heat engine undergoing the Otto Cycle
    a) The gas absorbs heat, at constant volume between 120'C and 300'C
    b) The gas expands adiabatically from V1 to V2 = 5V1
    c) The gas cools, at constant volume to Td at point D where the pressure is 1At
    d) The gas is then adiabatically compressed from V2 to V1 returning to the original temperature of 120'C
    You may assume Cv = 5R/2 and Cp = 7R/2

    What are the pressures and temperatures (in Kelvin) at points A,B,C,D?


    2. Relevant equations

    Ideal gas law pV = nRT
    Charle's law = V1/T1 = K and V1/T1 = V2/T2
    Boyle's law = P1V1 = P2V2


    3. The attempt at a solution

    Temperatures
    A = 120 + 273.15 = 393.15K
    B = 300 + 273.15 = 573.15K
    C =
    D =

    Pressure
    A =
    B =
    C = 1At
    D =

    I'm guessing i'm going to have to use Boyle's and Charle's laws in order to fill in the blanks.

    V1 / 573.15 = 5V1 / T2

    T2 / 573.15 = 5V1 / V1

    T2 / 573.15 = 4V1

    But here's the problem, it doesn't appear like this is going to solve anything. I reach this barrier for the other blanks as well. Could someone possibly edge me in the right direction please?

    Thanks
     
    Last edited: Nov 13, 2008
  2. jcsd
  3. Nov 13, 2008 #2

    Andrew Mason

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    Boyle's law only works if T is the same. It isn't. Charle's law only works if P is constant. It isn't.

    You have to use the first law of thermodynamics: dQ = dU + dW and the adiabatic condition [itex]PV^\gamma = K[/itex] where [itex]\gamma[/itex] is the ratio Cp/Cv for air (1.4).

    AM
     
  4. Nov 13, 2008 #3
    So basically, if I can find out what K is from the Adiabatic condition, then I should be able to calculate the values of P and V for the other points?

    Except I don't have a point which has both P and V values.
     
  5. Nov 13, 2008 #4

    Andrew Mason

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    Sure you do. You know that V = nRT/P. So if V is constant (ie. A to B) nRT/P is constant. You know T so you can work out P at point B.

    So you can calculate [itex]PV^\gamma[/itex] for point B and, therefore, for point C.

    AM
     
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