Chapter 20, Problem 7P

(III) The operation of a diesel engine can be idealized by the cycle shown in Fig. 20-18. Air is drawn into the cylinder during the intake stroke (not part of the idealized cycle). The air is compressed adiabatically, path ab. At point b diesel fuel is injected into the cylinder which immediately burns since the temperature is very high. Combustion is slow, and during the first part of the power stroke, the gas expands at (nearly) constant pressure, path bc. After burning, the rest of the power stroke is adiabatic, path ed. Path da corresponds to the exhaust stroke. (a) Show that, for a quasistatic reversible engine undergoing this cycle using an ideal gas, the ideal efficiency is

$e=1\frac{{(V_a/V_c)}^{-\gamma }-{(V_a/V_b)}^{-}{}^{\gamma }}{\gamma [{(V_a/V_c)}^{-1}-{(V_a/V_b)}^{-1}]},$

where $V_{\text{a}}/V_{\text{b}}$ is the “compression ratio”. $V_{\text{a}}/V_{\text{c}}$ is the “expansion ratio”, and γ is defined by Eq. 19-14.(b) If $V_{\text{a}}/V_{\text{b}}$ = 16 and $V_{\text{a}}/V_{\text{c}}$ = 4.5, Calculate the efficiency assuming the gas is diatomic (like N₂ and O₂?) and ideal.

FIGURE 20-18

Problem 7.