$1.)$ A submerged combustion burner $($as shown below$)$ is used to produce hot water. A gas$-$phase fuel is

burned with $5\%$ excess air $($both enter at $77F).$ The fuel has a composition of $75wt\%C$ and $25wt\%H,$

and the $HHV$ is $23,920Bt\frac{u}{l}b.$ Flue gas leaves the vessel at $300F$ and $7\mathrm{.}5$atm and in equilibrium with the

hot water leaving the vessel $($some of the hot water will evaporate join the water vapor already in flue gas

coming out of the burner$).$ Assume complete combustion $(100\%$ conversion of fuel plus no CO

produced$).$ Feedwater is added at $190F$ and is heated to $300F$ by the combustion reaction $($the hot water

exits the bottom in the liquid phase due to the high pressure$).$ The heat of vaporization of water at $77F$ is

$18,937Bt\frac{u}{l}$bmol.

$($a$)$ What is the LHV of the fuel $($Btu$/$lb$)?$

$($b$)$ Find the lbmoles of all components that exit the burner $($upwards arrows$)$ per pound of fuel before the

water evaporates $($i$.$e$.$ ignore the presence of the liquid water and just do a material balance on the burner$).$

$($c$)$ Calculate the pounds of liquid water that evaporate and leave with the flue gas per pound of fuel.

$($d$)$ Calculate the pounds of hot water produced per pound of fuel. Make sure to include an enthalpy input$-$

output table and be very clear about the reference states that you use. Recall that the heat capacity for

liquid water is $1Bt\frac{u}{l}bF.$ Assume that the system is well insulated. Neglect pressure effects in your

energy balance.