$(30\%)$ It is known that a fuel has the following chemical composition, $C_3{H}_{}$ :

$($a$)$ Derive the stoichiometric combustion equation for the combustion of this fuel $($with

the unknown, $).$ You can use $4$:$1$ ratio for $N_2$ and $O_2$ for simplicity.

$($b$)$ Determine $$ if this fuel's LHV is $)$ lower than its HHV$.$ Latent heat of

evaporation is $2\mathrm{.}44M\frac{J}{k}g.$

$($c$)$ If we want to generate an adiabatic flame temperature of $2,000K$ burning the fuel

$CH4,$ what is the percentage $(\%)$ of stoichiometric air is needed. $($heat of formation $C{H}_4$ :

$-74\mathrm{.}85M\frac{J}{k}$mol, and it is known that a lean rich burning is used$).$