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Homework Help: Efficiency of a Diesel Engine

  1. Nov 19, 2008 #1
    1. The problem statement, all variables and given/known data

    The figure shows the thermodynamic cycle of a diesel engine. This cycle differs from that of a gasoline engine in that combustion takes place isobarically. The compression ratio r is the ratio of maximum to minimum volume: r = V_1 /V_2. In addition, the so-called cutoff ratio is defined by r_c = V_3 /V_2.

    Find an expression for the engine's efficiency, in terms of the ratios r and r_c and the specific-heat ratio y. Although your expression suggests that the diesel engine might be less efficient than the gasoline engine , the diesel's higher compression ratio more than compensates, giving it a higher efficiency (the ratio of the work delivered to the heat extracted during the combustion phase).

    http://img89.imageshack.us/img89/5663/rw1867sf0.th.jpg [Broken]http://g.imageshack.us/thpix.php [Broken]

    2. Relevant equations
    W = (p1v1 - p2v2) / (y-1)
    e = W / Q_h

    3. The attempt at a solution
    Q_h = p(V_3 - V_2)
    W_12 = (p_1 V_1 - p_2 V_2) / (y - 1)
    W_23 = p(V_3 - V_2) (though I think this one is not work delivered)
    W_34 = (p_3 V_3 - p_4 V_4) / (y - 1)
    W_41 = 0

    W = (p_1 V_1 - p_2 V_2) / (y - 1) + (p_3 V_3 - p_4 V_4) / (y - 1)
    = (p_1 V_1 - p_2 V_2 + p_3 V_3 - p_4 V_4) / (y - 1)

    e = (p_1 V_1 - p_2 V_2 + p_3 V_3 - p_4 V_4) / [(y - 1) (p (V_3 - V_2))]

    Since p_2 and p_3 are the same, this simplifies to...

    e = (p_1 V_1 + p (V_3 - V_2) - p_4 V_4) / [(y - 1) (p (V_3 - V_2))]

    Now, p_4 is not given and I cannot eliminate it so I don't know how to proceed from here. Please help.
    Last edited by a moderator: May 3, 2017
  2. jcsd
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