$(30$ pts$.)$ Consider a fuel which is an equimolar mixture of propane $(C_3{H}_8)$ and isooctane

$(C_8{H}_{18}).$

a$.$ Write out the complete stoichiometric combustion reaction for this fuel burning with

air and determine the stoichiometric air$-$fuel ratio on a molar basis and a mass basis.

b$.$ Determine the air$-$fuel ratio for combustion at an equivalence ratio of $0\mathrm{.}8.$

c$.$ Determine the enthalpy of the products of an ideal $($complete$)$ combustion at an

equivalence ratio of $0\mathrm{.}8.$ The products are assumed to be at $1500$ K and $1$ atm $.$

Express your result as enthalpy per unit mass of fuel.