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

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$\textbf{\large Part A}$

$\text{The general form of the reaction can be written as follows:}$

\begin{align*} 0.4\text{C}_{3}\text{H}_{8}+0.6\text{CH}_{4}+a(\text{O}_{2}+3.76\text{N}_{2})\:->b\text{CO}_{2}+c\text{H}_{2}\text{O}+d\text{N}_{2} \end{align*}

An analysis of the reaction gives the following values for the coefficients:

\begin{align*} &a=3.2\\ &b=1.8\\ &c=2.8\\ &d=12.032 \end{align*}

$\text{The final form of the reaction is then:}$

\begin{align*} 0.4\text{C}_{3}\text{H}_{8}+0.6\text{CH}_{4}+3.2\text{O}_{2}+12.032\text{N}_{2}\:->1.8\text{CO}_{2}+2.8\text{H}_{2}\text{O}+12.032\text{N}_{2} \end{align*}

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