$8)$ During the power stroke in a four$-$stroke automobile engine, the piston is forced

down as the mixture of combustion products and air undergoes an adiabatic expansion. Assume $(1)$ the engine is running at r $[$cycles$/$min$]$; $(2)$ the gauge pressure immediately before the expansion is P $[$atm$]$; $(3)$ the volumes of the mixture immediately before and after the expansion are V$1[$cm$^3]$ and V$2[$cm$^3],$ respectively; $(4)$ the time interval for the expansion is one$-$fourth that of the total cycle; and $(5)$ the mixture behaves like an ideal gas with specific heat ratio Y$.$ Find the average power generated during the power stroke.