Problem $1$: $(10$ pts$)$ The power delivered by the engine in a Cessna Skyhawk $4-$seater airplane is $100$ kW $,$ at a thermal efficiency of $25\%.$ Heat supplied for the engine comes from burning fuel, which releases $40,000k\frac{J}{k}g$ when it burns. The cruising speed of the plane is $160$ mph and the density of the fuel is $0\mathrm{.}8$ kg$/$L$.$

$($Note: $1$gal$=3\mathrm{.}785L,1mph=0\mathrm{.}447\frac{m}{s},1hr=3600s$

$($a$)$ Find the hourly fuel consumption of the airplane in $k\frac{g}{h}r$ and $ga\frac{l}{h}r.$

$($b$)$ Find the heating power rejected by the engine exhaust and cooling fins.

$($c$)$ Estimate the miles per gallon achieved by this airplane.