$(45$ points$)$ Ethane is to be burned with $50\mathrm{.}0\%$ excess air in a boiler furnace. Ethane and air components may be assumed to have the following constant values:

$C_{p,N_2}=31\mathrm{.}3\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

$C_{p,C_2}=50\mathrm{.}0\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

$C_{p,H_{2}O(v)}=38\mathrm{.}5\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

$C_{p,O_2}=33\mathrm{.}1\frac{J}{\text{m}\text{o}\text{l}\text{.}K}$

Taking as a basis of calculation $1\mathrm{.}0$moloftheethanefedtothefurnacedrawandlabela flowchart of the process.

b$.$ Perform all required material balance calculations.

c$.$ Write the energy balance for the process.

d$.$ Assuming complete combustion of the fuel, calculate the adiabatic flame temperature, $T_{ad},$ in $C.$