A spark$-$ignition engine is throttled when operating at part load $($the inlet pressure is reduced$)$ while the fuel$/$air ratio is held essentially constant. Part$-$load operation of the engine is modeled by the cycle shown in Fig. $5-2$d; the inlet air is at pressure P$1$ the exhaust pressure is atmospheric Pa$,$ and the ambient temperature is Ta$.$ Derive an expression for the decrease in net indicated fuel conversion efficiency due to throttling from the ideal constant$-$volume cycle efficiency and show that it is proportional to $($Pa$/$P$1-1).$ Assume mass fuel $$ mass air.