A constant-volume tank contains a mixture of $\mathrm{I} \mathrm{~kmol}$ of benzene $\left(\mathrm{C}_{0} \mathrm{H}_{0}\right)$ gas and $30$ percent excess air at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$. The contents of the tank are now ignited, and all the hydrogen in the fuel burns to $\mathrm{H}_{2} \mathrm{O}$ but only $92$ percent of the carbon burns to $\mathrm{CO}_{2}$, the remaining $8$ percent forming $\mathrm{CO}$. If the final temperature in the tank is $1000 \mathrm{~K}$, Find the heat transfer from the combustion chamber during this process.

Gaseous E10 fuel is 10 percent ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\right)$ and 90 percent octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ on a kmol basis. This fuel is burned with 110 percent theoretical air. During the combustion process, 90 percent of the carbon in the fuel is converted to $\mathrm{CO}_{2}$ and 10 percent is converted to CO. Determine (a) the balanced combustion equation, (b) the dew-point temperature of the products, in $^{\circ} \mathrm{C}$, for a product pressure of 100 kPa, (c) the heat transfer for the process, in kJ, after 2.5 kg of fuel are burned and the reactants and products are at $25^{\circ} \mathrm{C}$ with the water in the products remaining a gas, and (d) the relative humidity of atmospheric air for the case where the atmospheric air is at $25^{\circ} \mathrm{C}$ and 100 kPa and the products are found to contain 9.57 kmol of water vapor per kmol of fuel burned.

$$\begin{matrix} \text{} & \text{}{\bar{h}_{f}^{\circ}, \mathrm{kJ} / \mathrm{kmol}} & \text{M, kg/kmol}\\ \text{}{\mathrm{C}_{3} \mathrm{H}_{18}(g)} & \text{-208,450} & \text{144}\\ \text{}{\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}(g)} & \text{-235,310 } & \text{46}\\ \text{}{\mathrm{CO}_{2}} & \text{-393,520} & \text{44}\\ \text{CO} & \text{-110,530} & \text{28}\\ \text{}{\mathrm{H}_{2} \mathrm{O}(g)} & \text{-241,820 } & \text{18}\\ \text{}{\mathrm{H}_{2} \mathrm{O}(\mathrm{l})} & \text{-285,830} & \text{18}\\ \text{}{\mathrm{O}_{2}} & \text{} & \text{32}\\ \text{}{\mathrm{N}_{2}} & \text{} & \text{28}\\ \end{matrix}$$

A gaseous fuel mixture that is 40 percent propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ and 60 percent methane $\left(\mathrm{CH}_{4}\right)$ by volume is mixed with the theoretical amount of dry air and burned in a steady-flow, constant-pressure process at 100 kPa. Both the fuel and air enter the combustion chamber at 298 K and undergo a complete combustion process. The products leave the combustion chamber at 398 K. Determine (a) the balanced combustion equation, (b) the amount of water vapor condensed from the products, and (c) the required airflow rate, in kg/h, when the combustion process produces a heat transfer output of 97,000 kJ/h.

$$\begin{matrix} \text{ } & \text{$\bar{h}_{f}^{\circ}, \mathrm{kJ} / \mathrm{kmol}$} & \text{$M,$ kg/kmol} & \text{$\bar{c}_{p}, \mathrm{kJ} / \mathrm{kmol} \cdot \mathrm{K}$}\\ \hline \text{$\mathrm{C}_{3} \mathrm{H}_{8}(g)$} & \text{$-103,850$} & \text{44} & \text{ }\\ \text{$\mathrm{CH}_{4}(g)$} & \text{$-74,850$} & \text{16} & \text{ }\\ \text{$\mathrm{CO}_{2}$} & \text{$-393,520$} & \text{44} & \text{41.16}\\ \text{$\mathrm{CO}$} & \text{$-110,530$} & \text{28} & \text{29.21}\\ \text{$\mathrm{H}_{2} \mathrm{O}(g)$} & \text{$-241,820$} & \text{18} & \text{34.28}\\ \text{$\mathrm{H}_{2} \mathrm{O}(l)$} & \text{$-285,830$} & \text{18} & \text{75.24}\\ \text{$\mathrm{O}_{2}$} & \text{ } & \text{32} & \text{30.14}\\ \text{$\mathrm{N}_{2}$} & \text{ } & \text{28} & \text{29.27}\\ \end{matrix}$$

Gaseous propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ is burned in a steady-flow, constant-pressure process at 100 kPa with 200 percent theoretical air. During the combustion process, 90 percent of the carbon in the fuel is converted to $\mathrm{CO}_{2}$ and 10 percent is converted to CO. Determine (a) the balanced combustion equation, (b) the dew-point temperature of the products, in $^{\circ} \mathrm{C},$ and (c) the heat transfer from the combustion chamber, in kJ, after 100 kmol of fuel are burned when the reactants enter the combustion chamber at $25^{\circ} \mathrm{C}$ and the products are cooled to $25^{\circ} \mathrm{C}.$

$$\begin{matrix} \text{ } & \text{$\bar{h}_{f}^{\circ},\ \mathrm{kJ}/ \mathrm{kmol}$}\\ \hline \text{$\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})$} & \text{$-103,850$}\\ \text{$\mathrm{CO}_{2}$} & \text{$-393,520$}\\ \text{$\mathrm{CO}$} & \text{$-110,530$}\\ \text{$\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$} & \text{$-241,820$}\\ \text{$\mathrm{H}_{2} \mathrm{O}(l)$} & \text{$-285,830$}\\ \end{matrix}$$

Octane gas $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ at $25^{\circ} \mathrm{C}$ is burned steadily with 80 percent excess air at $25^{\circ} \mathrm{C},$ 1 atm, and 40 percent relative humidity. Assuming combustion is complete and the products leave the combustion chamber at 1000 K, determine the heat transfer for this process per unit mass of octane.

A coal from Texas which has an ultimate analysis (by mass) of 39.25 percent C, 6.93 percent $H_{2},$ 41.11 percent $O_{2},$ 0.72 percent $N_{2},$ 0.79 percent S, and 11.20 percent ash (non-combustibles) is burned steadily with 40 percent excess air in a power plant boiler. The coal and air enter this boiler at standard conditions, and the products of combustion in the smokestack are at $127^{\circ} \mathrm{C}.$ Calculate the heat transfer, in kJ/kg fuel, in this boiler. Include the effect of the sulfur in the energy analysis by noting that sulfur dioxide has an enthalpy of formation of -297,100 kJ/kmol and an average specific heat at constant pressure of $c_{p}=41.7\ \mathrm{kJ} / \mathrm{kmol} \cdot \mathrm{K}.$

Diesel fuel $\left(\mathrm{C}_{12} \mathrm{H}_{26}\right)$ at $77^{\circ} \mathrm{F}$ is burned in a steadyflow combustion chamber with 20 percent excess air that also enters at $77^{\circ} \mathrm{F}$. The products leave the combustion chamber at $800 \mathrm{~R}$. Assuming combustion is complete, Find the required mass flow rate of the diesel fuel to supply heat at a rate of $1800 \mathrm{~Btu} / \mathrm{s}$.

Methane $\left(\mathrm{CH}_{4}\right)$ is burned completely with the stoichiometric amount of air during a steady-flow combustion process. If both the reactants and the products are maintained at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ and the water in the products exists in the liquid form, Find the heat transfer from the combustion chamber during this process. What would your answer be if combustion were achieved with $100$ percent excess air?

What does the dew-point temperature of the product gases represent? How is it determined?

Propane fuel $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ at $25^{\circ} \mathrm{C}$ is mixed steadily with $50$ percent excess air at $500^{\circ} \mathrm{C}$ in an atmospheric pressure combustor. Combustion products leave at $1500^{\circ} \mathrm{C}$, and the volumetric flow rate of the air is $1 \mathrm{~m}^{3} / \mathrm{s}$. Find the rate of heat transfer in this combustor.

$\mathrm{n}$-Octane gas $\left(\mathrm{C}_8 \mathrm{H}_{18}\right)$ is burned with $100$ percent excess air in a constant pressure burner. The air and fuel enter this burner steadily at standard conditions and the products of combustion leave at $257^{\circ} \mathrm{C}$. Calculate the heat transfer, in $\mathrm{kJ} / \mathrm{kg}$ fuel, during this combustion.

Propane fuel $\left(\mathrm{C}_{3} \mathrm{H}_{2}\right)$ is burned with an air-fuel ratio of 25 in an atmospheric pressure heating furnace. Determine the heat transfer per kilogram of fuel burned when the temperature of the products is such that liquid water just begins to form in the products.

Consider a complete combustion process during which the reactants enter the combustion chamber at $20^{\circ} \mathrm{C}$ and the products leave at $700^{\circ} \mathrm{C}.$ Combustion is achieved with (a) 100 percent theoretical air, (b) 200 percent theoretical air, and (c) the chemically correct amount of pure oxygen. For which case will the amount of heat transfer be the lowest? Explain.

Consider a complete combustion process during which both the reactants and the products are maintained at the same state. Combustion is achieved with (a) 100 percent theoretical air. (b) 200 percent theoretical air, and (c) the chemically correct amount of pure oxygen. For which case will the amount of heat transfer be the highest? Explain.