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.

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

Propane fuel $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ is burned in a space heater with 50 percent excess air. The fuel and air enter this heater steadily at 1 atm and $17^{\circ} \mathrm{C},$ while the combustion products leave at 1 atm and $97^{\circ} \mathrm{C}.$ Calculate the heat transferred in this heater, in kJ/kmol fuel.

Show that the number is rational by writing it as a quotient of two integers. 1

Liquid propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ enters a combustion chamber at $25^{\circ} \mathrm{C}$ at a rate of 1.2 kg/mm where it is mixed and burned with 150 percent excess air that enters the combustion chamber at $12^{\circ} \mathrm{C}.$ If the combustion is complete and the exit temperature of the combustion gases is 1200 K, determine (a) the mass flow rate of air and (b) the rate of heat transfer from the combustion chamber.

What does 100 percent theoretical air represent?

Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. During the process, 30 kJ of heat is transferred to the water, and 5 kJ of heat is lost to the surrounding air. The paddle-wheel work amounts to 500 Nm. Determine the final energy of the system if its initial energy is 12.5 kJ.

Butane is burned with dry air at 40$^{\circ} \mathrm{C}$, 100 kPa, with AF = 22 on a mass basis. For complete combustion, find the equivalence ratio, the percentage of theoretical air, and the dew point of the products. How much water (kg/kg fuel) is condensed out, if any, when the products are cooled down to ambient temperature, 40$^{\circ} \mathrm{C}$?

The percentage p(t) of children who can speak in at least single words by the age of t months can be approximated by the equation $p(t)=100\left(1-\frac{12,200}{t^{4.48}}\right) \quad(t \geq 8.5)$ a. Give a technology formula for p. b. Graph p for $8.5 \leq t \leq 20$ and $0 \leq p \leq 100$. c. Create a table of values of p for t=9, 10, ..., 20 (rounding answers to one decimal place). d. What percentage of children can speak in at least single words by the age of 12 months? e. By what age are 90% or more children speaking in at least single words?

Ethylene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ is burned with 175 percent theoretical air during a combustion process. Assuming complete combustion and a total pressure of 14.5 psia, determine (a) the air-fuel ratio and (b) the dew-point temperature of the products.

Ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ is burned at atmospheric pressure with the stoichiometric amount of air as the oxidizer. Determine the heat rejected, in kJ/kmol fuel, when the products and reactants are at $25^{\circ} \mathrm{C},$ and the water appears in the products as water vapor.

Determine whether

$$\Delta A B C , \text { with } \Lambda = 110 ^ { \circ } , a = 16 \ and \ b = 21,$$

has no solution, one solution, or two solutions. Then solve the triangle, it possible. Round measures of sides to Ihe nearest tenth and measures of angles to the nearest degree.

Methyl alcohol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ is burned with 50 percent excess air. The combustion is incomplete with 10 percent of the carbon in the fuel forming carbon monoxide. Calculate the mole fraction of carbon monoxide and the apparent molecular weight of the products.

Solve each equation by graphing.Round to the nearest hundredth, if necessary. $3 x^{3}-x^{2}+8 x=15$

When comparing his check register to his bank statement, Donte found that he had failed to record deposits of $55.65,$103.50, and $25.00. What is the total of these amounts and how will he use this information to reconcile his account?