Combustion gas containing $20\%($volume ratio$)C{H}_4,40\%C_2{H}_6$ and $40\%C_3{H}_8,$ is fed to a boiler where it is burnt with sufficient air $($no excess $O_2).$ The combustion gas is supplied to the boiler at $20C$ and the air enters at a temperature of $220C.$ The boiler stack temperature is $420C.$

$($a$)$ Draw a schematic diagram of the process and calculate the standard combustion enthalpies for methane, ethylene, and propane.

$($b$)$ Write the mole balance of the inlet and outlet of the boiler. Calculate the energy balance of the combustion reactions taking place inside the boiler and use tables to show the results.

$($c$)$ The heat generated from the boiler is used to warm up water in a standard swimming pool of $2500m^3$ from $10C$ to $30C,$ assuming $100\%$ heat exchange efficiency. Calculate the volume of $C{O}_2$ that will be released from the boiler into the environment at $20C.$

NOTE:

For full marks, draw a schematic diagram of the process including the balanced combustion reactions. Write down clearly all the assumptions used to solve the problem.

Relevant Data at $20C$ :

The standard state of all reactants and products is gaseous.

Air consists of $21\%O_2$ and $79\%N_2$ on a volume basis.

Ideal gas constant: $8\mathrm{.}314Jmo{l}^{-1}{K}^{-1}.$

Atmospheric pressure: $101\mathrm{.}3$kPa.

Density of water: $997kg{m}^{-3}.$

$C_p(O_2$ gas $)=30Jmo{l}^{-1}{K}^{-1}$

$C_p(N_2$ gas $)=30Jmo{l}^{-1}{K}^{-1}$

$C_p(H_{2}O$ gas $)=35Jmo{l}^{-1}{K}^{-1}$

$C_p(H_{2}O$ liquid $)=4\mathrm{.}18kJmo{l}^{-1}{K}^{-1}$

$C_p(C{O}_2$ gas $)=39Jmo{l}^{-1}{K}^{-1}$

$C_p(C{H}_4$ gas $)=35\mathrm{.}7Jmo{l}^{-1}{K}^{-1}$

$C_p(C_2{H}_6$ gas $)=52\mathrm{.}5Jmo{l}^{-1}{K}^{-1}$

$C_p(C_3{H}_8$ gas $)=73\mathrm{.}6Jmo{l}^{-1}{K}^{-1}$

$H{?}_f(C{H}_4$ gas $)=-74\mathrm{.}5kJmo{l}^{-1}$

$H{?}_f(C_3{H}_8$ gas $)=-103\mathrm{.}8kJmo{l}^{-1}$

$H{?}_f(C{O}_2$ gas $)=-393\mathrm{.}5kJmo{l}^{-1}$

$H{f}_f(H_{2}O$ gas $)=-241\mathrm{.}8kJmo{l}^{-1}$

$H{?}_f(C_2{H}_6$ gas $)=-83\mathrm{.}8kJmo{l}^{-1}$