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Volumes at C and D in a Carnot cycle

  1. Jun 8, 2015 #1
    1. The problem statement, all variables and given/known data
    A Carnot cycle, shown in Fig. 20-7, has the following conditions: Va = 7.5 L, Vb = 15 L, TH = 470°C, and TL = 260°C. The gas used in the cycle is 0.50 mil of a diatomic gas, y = 1.4. Calculate (a) the pressures at a and b; (b) the volumes at c and d. (The rest of the problem...)

    2. Relevant equations
    PVy = Constant

    3. The attempt at a solution
    I already solved part (a), with Pa = 4.1 x 105 Pa and Pb = 2.1 x 105 Pa.

    For part (b), I tried
    PVy = constant
    nRT⋅Vy-1 = constant.

    Annnnd then I get lost. I don't understand what constant represents or if I am even on the right track. The book says Vc = 34 L and Vd = 17 L.
     
  2. jcsd
  3. Jun 8, 2015 #2

    vela

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    What do the points a, b, c, and d represent in the Carnot cycle? You didn't post the figure.
     
  4. Jun 8, 2015 #3
    My apologies, here is the figure:

    n1723o.png

    Points a, b, c, and d represent stages of the Carnot engine as it works.
     
  5. Jun 8, 2015 #4

    vela

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    For an adiabatic process, you have ##PV^\gamma = \text{constant}##. Since points b and c are on the same adiabat, you can say that ##P_b V_b^\gamma = P_c V_c^\gamma##.

    If it still seems confusing, consider the analogous situation for an isothermal process. The righthand side of the ideal gas law, ##PV = nRT##, is constant for an isothermal process. In other words, on an isotherm, we have that ##PV = \text{constant}##. Points a and b are on the same isotherm, so you can say ##P_a V_a = P_b V_b##, which should look very familiar to you.
     
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