$-$ A standard air$-$driven diesel cycle has a compression ratio of $18\mathrm{.}2.$ The air is at $540$R and $14\mathrm{.}7$ psia at the beginning of the compression process, and at $3000$R at the end of the heat addition process. Assuming constant specific heats, determine $($a$)$ the cutoff ratio; $($b$)$ the heat rejection per unit mass; $($c$)$ the thermal efficiency. Assume cp $=0\mathrm{.}24$ Btu$/$lbm$.$R; cv $=0\mathrm{.}171$ Btu$/$lbm$.$R; k $=1\mathrm{.}4($do not use thermodynamic tables$)$