Question $1[40$ marks $]$

Natural gas is modelled as pure methane $(C{H}_4)$ and is supplied to a combustor where it is burned with air $(79$:$21$ molar ratio of $N_2$ and $O_2).$ Both fuel and air enter at a temperature of $298K$ and pressure of $101,325Pa.$ The combustor can be modelled as operating adiabatically and at constant pressure.

$($a$)$ Determine the equivalence ratio $()$ required to give an $O_2$ mole fraction of $10\%$ in the products of combustion. Clearly state all assumptions you make in solving the problem.

$[16$ marks$]$

A proposed low$-$emissions fuel comprises a $50$:$50$ molar ratio of $C{H}_4$ and $H_2.$

$($b$)$ Calculate the $C{O}_2$ emission factor $(E_{CO},$ mass of $C{O}_2$ emitted per unit thermal energy released in units of $gC\frac{O_2}{M}J)$ of the low$-$emission fuel.

$[12$ marks$]$

$($c$)$ Calculate the product temperature, $T_P,$ if the low$-$emissions fuel is burned at an equivalence ratio of $0\mathrm{.}7.$

$[12$ marks$]$

Table Q$1$

$\backslash$table$[[,$CH$\_(4),$H$\_(2),$O$\_(2),$N$\_(2),$CO$\_(2),$H$\_(2)$O$],[$Molar weight $($g$/$mol$),16,2,32,28,44,18],[$Lower heating value $($MJ$/$kg$),50,120,-,-,-,-],[$Molar heat capacity $($Jmol$^(-1)$K$^(-1))],[$Temperature $($K$),$CH$\_(4),$H$\_(2),$O$\_(2),$N$\_(2),$CO$\_(2),$H$\_(2)$O$],[600,52\mathrm{.}74,29\mathrm{.}32,32\mathrm{.}11,30\mathrm{.}10,47\mathrm{.}32,36\mathrm{.}32],[800,64\mathrm{.}08,29\mathrm{.}62,33\mathrm{.}74,31\mathrm{.}44,51\mathrm{.}44,38\mathrm{.}74],[1,000,73\mathrm{.}75,30\mathrm{.}20,34\mathrm{.}86,32\mathrm{.}69,54\mathrm{.}30,41\mathrm{.}27],[1,200,\backslash$table$[[81\mathrm{.}68]],30\mathrm{.}99,35\mathrm{.}66,33\mathrm{.}72,56\mathrm{.}35,43\mathrm{.}75],[1,400,88\mathrm{.}11,31\mathrm{.}86,36\mathrm{.}28,34\mathrm{.}52,57\mathrm{.}83,46\mathrm{.}06],[1,600,93\mathrm{.}33,32\mathrm{.}73,36\mathrm{.}80,35\mathrm{.}13,58\mathrm{.}90,48\mathrm{.}07],[1,800,97\mathrm{.}63,33\mathrm{.}54,37\mathrm{.}27,35\mathrm{.}59,59\mathrm{.}70,49\mathrm{.}75],[2,000,101\mathrm{.}24,34\mathrm{.}28,37\mathrm{.}75,35\mathrm{.}98,60\mathrm{.}34,51\mathrm{.}20],[2,200,104\mathrm{.}31,34\mathrm{.}95,38\mathrm{.}19,36\mathrm{.}27,60\mathrm{.}85,52\mathrm{.}41],[2,400,107\mathrm{.}00,35\mathrm{.}56,38\mathrm{.}63,\backslash$table$[[36\mathrm{.}51]],61\mathrm{.}28,53\mathrm{.}44],[2,600,109\mathrm{.}39,36\mathrm{.}11,39\mathrm{.}07,\backslash$table$[[36\mathrm{.}71]],61\mathrm{.}64,54\mathrm{.}32]]$