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Efficiency of Diesel cycle

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Derive a formula for the efficiency of the Diesel cycle, in terms of the compression ratio V1/V2

    2. Relevant equations

    e=[itex]\frac{W}{Q_{h}}[/itex]
    w= ∫pdV



    3. The attempt at a solution

    Now I know I should have used e=1-[itex]\frac{Q_{c}}{Q_{h}}[/itex] to get it but he said it is possible using e=[itex]\frac{W}{Q_{h}}[/itex]

    I know that W_{4-1} is equal to zero and W_{2-3} is equal to P_{2}(V_{3}-V_{2})

    what I don't know is how he got

    W_{1-2} = [itex]\frac{e}{1-δ}[/itex]*cv[itex]^{-δ+1}[/itex] = [itex]\frac{1}{1-δ}[/itex]*(P_{2}V_{2}-P_{1}V_{1})

    and

    W_{3-1} = [itex]\frac{e}{1-δ}[/itex]*cv[itex]^{-δ+1}[/itex] = [itex]\frac{1}{1-δ}[/itex]*(P_{4}V_{4}-P_{3}V_{3})
     
  2. jcsd
  3. Apr 15, 2013 #2

    DrClaude

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    Staff: Mentor

    What are points 1,2,3, and 4? What is ##\delta##?
     
  4. Apr 15, 2013 #3
    1,2,3 and 4 are the strokes of the cycle. Well the different points on the picture. and δ is supposed to be gamma, which is the adiabatic exponent.

    I thought I could use

    W=∫pdV = C[itex]_{v}[/itex](T[itex]_{1}[/itex]-T[itex]_{2}[/itex]
    for the compression stroke...but I guess that is incorrect
     
  5. Apr 15, 2013 #4

    DrClaude

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    Staff: Mentor

    You have to be more specific. The numbering of points on a cycle is arbitrary. For each part of the cycle, state something like: 1→2 isothermal expansion at ##T_2##.
     
  6. Apr 15, 2013 #5
    From 1→2 is compression
    From 2→3 is fuel injection/combustion
    From 3→4 is the power stroke
    From 4→1 is exhaust
     
  7. Apr 15, 2013 #6

    Andrew Mason

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    Science Advisor
    Homework Helper

    The ideal diesel cycle consists of a constant pressure expansion (2-3) followed by an adiabatic expansion (3-4) followed by constant volume cooling (4-1) followed by adiabatic compression (1-2).

    So heat goes in only from 2-3 and heat goes out only from 4-1. Since W = Qh-Qc and η = W/Qh = 1-Qc/Qh you just have to deal with the two parts in which heat flows (ie. 4-1 and 2-3).

    Can you work out Qh and Qc? (hint: it involves temperature change and heat capacity).

    AM
     
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