Problem $1$:

An $8-$cylinder gasoline$-$fueled internal combustion engine was operated in atmospheric conditions of $\backslash (72^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ and $14\mathrm{.}6$ psia. The fuel had a density of $0\mathrm{.}79$ grams per milliliter and a Lower Heating Value of $46$ kilojoules per gram. The engine has a compression ratio given by the manufacturer of $9\mathrm{.}9.$ The operating manifold pressure is $10$ psig below ambient, and the operating fuel flow rate is $\backslash (200\backslash$mathrm$\{$~mL$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ The operating mass flow rate of air through the engine is $250$ grams per second. The constant$-$volume specific heat of air can be converted from $\backslash (0\mathrm{.}17\backslash$mathrm$\{$Btu$\}/\backslash$mathrm$\{$lbm$\}^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ to $\backslash (0\mathrm{.}4\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$g$\}^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$ If the fuel is expected to auto$-$ignite at cylinder pressures greater than $13,000$ psia, determine if the engine will experience autoignition. State the assumptions made in your analysis.