Q$1.$ Consider a combustion process starting from $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $1$ atm for two separated stoichiometric mixtures: a$)$heptane $\backslash (\backslash$left$(\backslash$mathrm$\{$C$\}\_\{7\}\backslash$mathrm$\{$H$\}\_\{16\}\backslash$right$)\backslash )$ and oxygen, and b$)$ hydrogen and oxygen. The lower heating values $($LHV$)$ and the average constant$-$pressure specific heats $\backslash (\backslash$left$(\backslash$bar$\{$c$\}\_\{$P$\}\backslash$right$)\backslash )$ from $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to the adiabatic flame temperature are shown in the Table below for the related species. Assume no dissociation in the combustion products.

$($a$)$ Calculate the adiabatic flame temperature at constant pressure for the stoichiometric nheptane and oxygen mixture.

$(10$ marks$)$

$($b$)$ Calculate the adiabatic flame temperature at constant pressure for the stoichiometric hydrogen and oxygen mixture.

$(6$ marks$)$

$($c$)$ Why are the answers to Part $($a$)$ and $($b$)$ substantially higher than the adiabatic flame temperature shown in the lecture slides, which is around $2000$ K with stoichiometric fuel$/$air mixture?

$(4$ marks$)$

$($d$)$ If $\backslash (\backslash$mathrm$\{$NO$\}\_\{$x$\}\backslash )$ emissions are to be reduced in an air$-$breathing engine, which fuel do you think is a better fuel to achieve this purpose? Explain why.

$(5$ marks$)$

Table for QI