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Cogeneration power cycle

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    A cogeneration power plant is operating in a thermodynamic cycle at steady state. The plant provides electricity to a community at a rate of 80 MW. The energy discharged from the power plant by heat transfer is denoted by [itex]\dot{Q}_{out}[/itex]. Of this, 70 MW is provided to the community for water heating and the remainder is discarded to the environment without use. The electricity is valued at $0.08 kW[itex]\cdot[/itex]h. If the cycle thermal efficiency is 40%, determine the (a) rate energy is added by heat transfer, [itex]\dot{Q}_{in}[/itex] in MW, (b) rate energy is discarded to the environment, in MW.


    2. Relevant equations
    [itex]W_{cycle} = Q_{in} - Q_{out}[/itex]
    [itex]\dot{Q}=\dot{W}[/itex]
    [itex]\eta = \frac{W_{cycle}}{Q_{in}}=\frac{Q_{in}-Q_{out}}{Q_{in}}[/itex]


    3. The attempt at a solution
    I haven't the slightest idea how to even start this. There aren't even any worked examples in the book. I only know that the rate of heat transfer has to be equal to 80 MW (the power supplied by the plant).
     
  2. jcsd
  3. Oct 30, 2011 #2

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    Homework Helper

    Welcome to PF, treynolds147! :smile:

    I think it's not the rate of heat transfer that is 80 MW.
    It's the generated useful power [itex]\dot W_{cycle}[/itex] that is 80 MW.
    With an [itex]\eta[/itex] of 40%, you should be able to find [itex]\dot Q_{in}[/itex].
     
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