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Otto Cycle problem

  1. Aug 28, 2016 #1
    hey my fellow ME please help me with this problem im stuck at.

    1. The problem statement, all variables and given/known data

    An Otto engine has a clearance volume of 7%. It produces 300 kW of power. What is the amount of heat rejected in kW?

    2. Relevant equations
    Wnet=Qadded-Qrejected
    (v2=Vc)Clearance Volume = (c)Clearance% x (Vd)Volume Displacement (v1-v2)
    math_957_3c600cab6023f52bbd29dc8318ec44c9.png where r is the compression ratio math_971_ce19de842ccd4fc0be69a9950897fdfd.png

    3. The attempt at a solution
    rk(compression ratio) = (c+1)/c stuck i dont know where to start
    then i should be able to solve the problem where Qrejected = Qadded - Work
     
    Last edited: Aug 28, 2016
  2. jcsd
  3. Aug 28, 2016 #2

    DrClaude

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    Staff: Mentor

    Your missing an equation for efficiency.
     
  4. Aug 28, 2016 #3
    i just edited it
     
  5. Aug 28, 2016 #4

    jack action

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    Science Advisor
    Gold Member

    Energy balance:
    [tex]\dot{W} = \dot{Q}_{in} - \dot{Q}_{out}[/tex]
    Efficiency definition:
    [tex]n_{th} = \frac{\dot{W}}{\dot{Q}_{in}}[/tex]
    Otto cycle efficiency:
    [tex]n_{th} = 1- \frac{1}{r^{(\gamma-1)}}[/tex]
    Compression ratio definition:
    [tex]r = \frac{V_d + V_{cc}}{V_{cc}}[/tex]
    You get 4 equations, 4 unknowns (##\dot{Q}_{in}##, ##\dot{Q}_{out}##, ##n_{th}##, ##r##), so you can resolve them. ##V_d## and ##V_{cc}## are not known but their ratio is given in the problem (and it is all that is really needed):
    [tex]0.07 = \frac{V_{cc}}{V_d}[/tex]
    (or it might be ##0.07 = \frac{V_{cc}}{V_d + V_{cc}}##; Not clear from the statement -> 7% of what?)
     
  6. Aug 28, 2016 #5
    7% clearance volume , clearance volume = cVd = c(v1-v2) so 0.07 = c(v1-v2)
     
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