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Thermodynamics engine question

  1. Nov 17, 2005 #1
    Ok, my question is as follows:

    An inventor claims to have developed an engine that takes in 10^8 J (Q_in) at a temperature of 400 K (T_2), and rejects 4x10^7 J (Q_out) to a reservoir of Temperatue of 200 K (T_1). The engine delivers 15 kilowatt hours of mechanical work (which = 3600 sec/hour *15 * 10^3 watts = 5.4x10^6 Joules). Would you advise investing money to put this engine on the market?

    the way i approached it was to calculate the max efficiency that a carnot engine would have, which is:

    efficiency = 1 - T_1/T_2 = 1 - 200/400 = 0.5 or 50%​

    Now, using the expression,
    Efficiency = Work output/Heat input​
    for the hypothetical engine gives. This gave me an efficiency of roughly 54%, and by Carnot's theorem, no engine can be more efficient than a carnot engine, or:

    Efficiency(carnot) > Efficiency(hypothetical)​
    and in this case, it doesnt hold, i.e.:
    50 % > 54 % is not true.​

    Is this the correct way to do this problem?
    Thanks
     
  2. jcsd
  3. Nov 17, 2005 #2

    Physics Monkey

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    I didn't check your number crunching, but you've approached the problem correctly.
     
  4. Nov 17, 2005 #3
    Thanks very much
     
  5. Nov 18, 2005 #4

    Andrew Mason

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    So what is your answer and why?

    My reason for not investing (besides the fact that the claim cannot be true as you have shown) would be: where are you going to find a reservoir to output at -73C?

    AM
     
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