$7$ A compression ignition engine for a small truck is to operate on an air$-$standard Dual cycle with a compression ratio of $\backslash ($ r$\_\{$c$\}=18\backslash ).$ Due to structural limitations$,$ maximum allowable pressure in the cycle will be $9000$ kPa $.$ Light diesel fuel is used at a fuel$-$air ratio of $\backslash (\backslash$mathrm$\{$FA$\}=0\mathrm{.}054\backslash ).$ Combustion efficiency can be considered $\backslash (100\backslash \%\backslash ).$ Cylinder conditions at the start of compression are $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $98$ kPa $.$ Calculate:

$($a$)$ Maximum indicated thermal efficiency possible with these conditions. $[\backslash \%]$

$($b$)$ Peak cycle temperature under conditions of part $($a$).[\backslash (\backslash$left$.\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash$right$]\backslash )$

$($c$)$ Minimum indicated thermal efficiency possible with these conditions. $[\backslash \%]$

$($d$)$ Peak cycle temperature under conditions of part $($c$).[\backslash (\backslash$left$.\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash$right$]\backslash )$