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Heat Engine/Thermodynamics

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    A heat engine is built to operate between temperatures of 1200 K and 300 K. It is used to lift a 30 kg mass at a constant velocity of 4 m/s.

    a) Determine the power that the heat engine must supply to lift the mass.

    b) Determine the maximum possible efficiency of the heat engine.

    c) If the engine were to operate at the maximum possible efficiency, determine the following:
    i. The rate at which the hot reservoir supplies heat to the engine.
    ii. The rate at which heat is exhausted to the cold reservoir.


    2. Relevant equations

    P = W/t
    e = 1 - T1/T2


    3. The attempt at a solution

    I figured out that (b) is 1 - (300/1200) = 75%.

    For (a), there is no distance stated to figure out work (W = Fd), and there is no time to determine power (P = W/t). What am I missing?
     
  2. jcsd
  3. Apr 26, 2009 #2

    rl.bhat

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    Power= rate of doing work. = Fd/t = fv.
     
  4. Apr 26, 2009 #3
    Oh! So, P = Fv = (30 kg)(9.8 m/s^2)(4 m/s) = 1176 J/s.

    So, if the power supplied to lift the mass is 1176 J/s, and the maximum possible efficiency is 75%, then the rate heat is removed from the hot reservoir.... Wouldn't that depend on the first law of thermodynamics?
    [delta]U = Q + W

    But how would you apply the equation exactly, and what would it signify?
     
  5. Apr 26, 2009 #4

    Andrew Mason

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    You do not need to apply the first law here. You just have to apply the efficiency. The work output is 1176 watts (J/s) at 75% efficiency (efficiency = work out/energy in) so the energy (heat flow) input must be...?

    AM
     
  6. Apr 26, 2009 #5
    So, given the equation e = W/QH...

    .75 = (1176W)/QH

    QH = 1568 W


    And, for the rate at which heat is exhausted to the cold reservoir, does this also depend on an efficiency equation?
     
    Last edited: Apr 26, 2009
  7. Apr 26, 2009 #6

    djeitnstine

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    75% = 75/100 = 0.75

    for rate at which heat is exhausted note that W = QH-QC. So dW/dt = dQH/dt - dQC/dt
     
  8. Apr 26, 2009 #7
    Hmm... Unfortunately, this is a non-calc based course, so would you know of another approach?
     
  9. Apr 26, 2009 #8

    djeitnstine

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    dW/dt = Power

    dQh/dt = rate of energy output from the hot resevior

    or perhaps delta Qh/ delta t which is average energy over a period of time

    similar argument for Qc
     
  10. Apr 26, 2009 #9
    Yes, but unfortunately, this is an algebra-based course. Is there another method for finding the rate at which heat is exhausted to the cold reservoir?
     
  11. Apr 26, 2009 #10

    Andrew Mason

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    W = Qh-Qc

    P = W/t = Qh/t - Qc/t

    You know two of those terms. So find Qc/t

    AM
     
  12. Apr 26, 2009 #11
    W = QH - QC

    392 W = 980 W - QC/t

    QC/t = 588 W

    Correct?
     
  13. Apr 26, 2009 #12

    Andrew Mason

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    I am not sure what you are doing here.

    W/t = 1176 w
    Qh/t = W/e = 1568 w

    AM
     
  14. Apr 26, 2009 #13
    My apologies. I was working on two similar problems... that's why the values were different.

    Thank you very much for your help! I appreciate it.

    -Science.girl
     
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