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Thermodynamics Power Cycle Energy Balance

  1. Jul 29, 2017 #1
    1. The problem statement, all variables and given/known data
    As shown in Fig. P5.39, a system undergoing a power cycle develops a net power output of 1 MW while receiving energy by heat transfer from steam condensing from saturated vapor to saturated liquid at a pressure of 100 kPa. Energy is discharged from the cycle by heat transfer to a nearby lake at 17°C. These are the only significant heat transfers. Kinetic and potential energy effects can be ignored. For operation at steady state, determine the minimum theoretical steam mass flow rate, in kg/s, required by any such cycle.

    Fig. 5.39: https://gyazo.com/49a3ca702a5fa239633f8f054618345e
    (Can't get it to embed)

    2. Relevant equations
    η = Wcycle / QH = 1 - TC / TH
    Wcycle = QH - QC
    mass flow: dmcv / dt = ∑ mi - ∑ me
    energy balance: dEcv / dt = Q - W + ∑ mi(hi + Vi2 / 2 + gzi)- ∑ me(he + Ve2 / 2 + gze)

    3. The attempt at a solution
    Knowing that the system operates at steady state, I know that the entry mass flow and exit mass flow are the same. I also know that since kinetic energy and potential energy can be ignored, the energy balance equation simplifies to:
    0 = Q - W + ∑ mi(hi)- ∑ me(he) =>
    W = Q + m(hi - he)

    Knowing that the initial and final states are at saturated vapor and saturated liquid, respectively, using the tables in the back of the book, I found the specific enthalpy values to be:
    h1 = 2675.5 kJ/kg
    h2 = 417.46 kJ/kg

    I know that I can use the thermal efficiency relation to find the QH value, but I don't know how exactly to find the thermal efficiency since there's no listed TH value, unless I'm missing something in the problem statement. I feel that the energy balance equation will be cake once the heat transfer value is found, but I just can't figure out how to get it. If anyone could steer me in the right direction, that would be appreciated.

    Edit: The temperature of the lake is 17°C, not 178C. Copy-and-paste didn't recognize the degree symbol.
     
    Last edited: Jul 29, 2017
  2. jcsd
  3. Jul 30, 2017 #2

    CWatters

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    Not my field but... isn't 100kPa about atmospheric pressure so the temperature of the steam would be...
     
  4. Jul 30, 2017 #3
    What would be the ratio of Qh to Qc if the system were operating reversibly (at maximum theoretical efficiency)? (Qh is the rate of heat addition from the steam reservoir).
     
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