$5\mathrm{.}17$ Consider the Lox$-$RP$-1$ propellant combination combusting at $100$ atmospheres with $=75.$

Determine the optimal mixture ratio by plotting $T_c,M($in chamber$),$ and $I_{spv}$ as a function of

$r$ for $Mvs.\frac{A}{A_t}=1,3,5,15,25,75r1\mathrm{.}5.At$ the optimal mixture ratio, plot $Mvs.\frac{A}{A_t}in$ the exit cone. Explain the behavior $of$ this curve. What recombination reactions are important? Tabulate the mass

fraction $of$ the six most prominent exhaust species $at=1,3,5,15,25,75,$ for the

optimal $r$ condition.