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Carnot Engine ~ Electric Generating station

  1. Feb 2, 2013 #1
    1. The problem statement, all variables and given/known data

    An electric generating station is designed to have an electric output power of 1.4 MW using a turbine with two-thirds efficiency of a Carnot engine. The Exhaust energy is transfered by heat to a cooling tower at 110°C.

    a) Find the rate at which the station exhausts energy by heat as a function of the fuel combustion temperature Th


    2. Relevant equations

    e= w/Qh=1-Qc/Qh , e_carnot=1-Tc/Th, P=W/t

    3. The attempt at a solution

    The only thing i have been able to figure out so far is e=(2/3)(1-(Tc/Th) Where Tc=383K

    I have been struggling with this one for quite some time and humbly asking for your help

    The book lists the answer as Qc/Δt=1.4((.5Th+383)/(Th-383))
    I am so confused....
     
  2. jcsd
  3. Feb 2, 2013 #2

    rude man

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    Book is right.

    What is the efficiency of a Carnot engine as a function of Th and Tc? Then, what is actual Qh and therefore actual Qc? Hint: use 1st law.
     
  4. Feb 2, 2013 #3
    I'm Sorry i'm still not following you....

    Man I feel like an idot.. What am i missing?
     
    Last edited: Feb 2, 2013
  5. Feb 2, 2013 #4

    Andrew Mason

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    If the output power is 1.4 MW what is the rate at which energy is input? Hint: efficiency = output/input = (dW/dt)/(dQh/dt)

    Once you get the rate of energy input, given the work output dW/dt = 1.4MW you can calculate the rate of exhaust energy Qc using W = Qh-Qc (i.e. dW/dt = dQh/dt - dQc/dt).

    Since efficiency is a function of Th (Tc=110C) you will have a Th in your answer. Be sure to use the Kelvin scale for T.
    AM
     
    Last edited: Feb 2, 2013
  6. Feb 2, 2013 #5

    rude man

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    <<What is the efficiency of a Carnot engine as a function of Th and Tc? Then, what is actual Qh and therefore actual Qc? Hint: use 1st law. >>Try to answer those two questions! The first is in your textbook. Call it e.

    Then, what does the 1st law say? How about Qh = Qc + W?
    For your system, efficiency = 2e/3 = e' so write Qh in terms of W and e'( Th, Tc).
    Then, solve for Qc. Realize that the answer to your problem is dQc/dt which will be in terms of dW/dt = P = 1.4MW as well as Th and Tc.

    I can say no more.
     
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