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Homework Help: Heat Engine Cycle Question

  1. Mar 6, 2010 #1
    1. The problem statement, all variables and given/known data

    21. A heat engine operates in a cycle between temperatures 700 K and 400 K. The heat input to the engine during each cycle is 2800 J. What is the maximum possible work done by the engine in each cycle?

    (A) 1200 J
    (B) 1600 J
    (C) 2100 J
    (D) 2800 J
    (E) 4400 J

    I believe that the answer is E. I just don't know how to prove it. If you could show that would be great. I know that



    2. Relevant equations

    e = |W|/|Qh|

    |Qh| = |W| + |Ql|

    e = 1 - |Ql|/|Qh|

    3. The attempt at a solution

    I'm lost...

    e = |W|/|Qh|

    |Qh| = |W| + |Ql|

    e = 1 - |Ql|/|Qh|

    I don't remember how to do this type of problem...
     
  2. jcsd
  3. Mar 6, 2010 #2
    Wait the answer is A... but why?
     
  4. Mar 7, 2010 #3

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    The maximum possible efficiency is in a reversible (Carnot) cycle. In a reversible cycle, [itex]\Delta S = 0[/itex], so [itex]\Delta S = \Delta S_h + \Delta S_c = -Q_h/T_h + Q_c/T_c = 0[/itex]. This means that [itex]Q_c/Q_h = T_c/T_h[/itex]

    So [itex]\eta = W/Q_h = (Q_h-Q_c)/Q_h = 1 - Q_c/Q_h = 1 - T_c/T_h[/itex]

    Plugging in the numbers: [itex]\eta = 1 - 400/700 = .42857[/itex].

    Since [itex]W = \eta * Q_h[/itex], the maximum Work is 1200 J. (.42857 * 2800).

    AM
     
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