Q$2(4$ points$)$

A conventional spark$-$ignition engine operating with gasoline will not run smoothly $($due to incomplete combustion$)$ with an equivalence ratio leaner than about $=0\mathrm{.}8.$ It is desirable to extend the smooth operating limit of the engine to leaner equivalence ratios so that at part$-$throttle operation $($with intake pressure less than $1$ atmosphere$)$ the pumping work is reduced.

Leaner than normal operation can be achieved by adding hydrogen gas $(H2)$ to the mixture in the intake system. The addition of H $2$ makes the fuel$-$air mixture easier to burn.

$($a$)$ The fuel composition with "mixed" fuel operation is $H2+C8H18-$one mole of hydrogen to every mole of gasoline, which is assumed the same as isooctane. What is the stoichiometric air$/$fuel ratio for the "mixed" fuel?

$($b$)$ The lower heating value of H $2$ is $120M\frac{J}{k}g$ and for isooctane is $44\mathrm{.}4$ MJJkg $.$ What is the heating value per kilogram of fuel mixture?