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Carnot Engine

  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    A Carnot heat engine operates between temperatures T1= 400K and T2= 300K. In each cycle the engine receives Qin=1200 J from the high temperature reservoir.
    a) Calculate the heat Qout delivered to the low temperature reservoir.
    b) Suppose the engine is operated in reverse as a refrigerator. Now the engine receives Qin= 1200 J from the low temperature reservoir. Determine the heat delivered to the high temperature reservoir.
    c) Calculate the work done by the engine in part a, and the work done on the refrigerator in part b. Note that both answers should be positive.
    d) Find the efficiency of the engine in part a, and the performance coefficient of the refrigerator in part b.

    2. Relevant equations
    QH+QC+W=0
    ##\frac{Q_H} {T_H}##+##\frac{Q_C} {T_C}##=0
    e=W/QH
    performance coefficient=##\frac{|Q_c|} {W}##
    3. The attempt at a solution

    My confusion arises when I get negative values for part c. Mathematically they should be negative, I suspect that I am not grasping a concept somewhere.
    20141004_152957.jpg
     
  2. jcsd
  3. Oct 4, 2014 #2

    Matterwave

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    Let's take the case for the engine first. Look at the diagram you drew at the top. Heat flows from the hot reservoir and a part of it is converted into work done by the engine, while the rest is dumped into the cold reservoir. This statement, translated into mathematical language says ##Q_h=W+Q_c## where ##Q_h,~Q_c,~W## are defined analogously from the above sentence with positive values corresponding to the bolded words. Does this equation make sense to you in terms of the language that it is translated to? Does the sign convention make sense to you?

    Now look at the equation you provided in your "relevant equations". You have the quite different equation ##Q_h+Q_c+W=0##, so again, looking at the picture you drew, what English sentence do you think this equation gets translated to?
     
  4. Oct 5, 2014 #3

    Andrew Mason

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    Your value for COP, .3333, is not correct. Since it is a Carnot cycle, COP = |Qc/W| = |Qc/(Qh-Qc)| = |Tc/(Th-Tc)|

    AM
     
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