Thermodynamics

758 | ThermodynamicsAssumptions 1 Combustion is complete. 2 Combustion gases are ideal gases.Analysis The combustion products contain CO 2 , H 2 O, N 2 , and some excessO 2 only. Then the combustion equation can be written asC 2 H 6 1.2a th 1O 2 3.76N 2 2 S 2CO 2 3H 2 O 0.2a th O 2 11.2 3.762a th N 2where a th is the stoichiometric coefficient for air. We have automaticallyaccounted for the 20 percent excess air by using the factor 1.2a th instead of a thfor air. The stoichiometric amount of oxygen (a th O 2 ) is used to oxidize the fuel,and the remaining excess amount (0.2a th O 2 ) appears in the products as unusedoxygen. Notice that the coefficient of N 2 is the same on both sides of the equation,and that we wrote the C and H balances directly since they are so obvious.The coefficient a th is determined from the O 2 balance to beO 2 :1.2a th 2 1.5 0.2a th S a th 3.5Substituting,C 2 H 6 4.2 1O 2 3.76N 2 2 S 2CO 2 3H 2 O 0.7O 2 15.79N 2(a) The air–fuel ratio is determined from Eq. 15–3 by taking the ratio of themass of the air to the mass of the fuel,AF m airm fuel 19.3 kg air/kg fuel14.2 4.76 kmol2129 kg>kmol212 kmol2 112 kg>kmol2 13 kmol2 12 kg>kmol2That is, 19.3 kg of air is supplied for each kilogram of fuel during this combustionprocess.(b) The dew-point temperature of the products is the temperature at whichthe water vapor in the products starts to condense as the products arecooled at constant pressure. Recall from Chap. 14 that the dew-point temperatureof a gas–vapor mixture is the saturation temperature of the watervapor corresponding to its partial pressure. Therefore, we need to determinethe partial pressure of the water vapor P v in the products first. Assumingideal-gas behavior for the combustion gases, we haveP v a N v3 kmolb1PN prod 2 a b1100 kPa2 13.96 kPaprod 21.49 kmolThus,T dp T sat @ 13.96 kPa 52.3°C(Table A–5)EXAMPLE 15–3Combustion of a Gaseous Fuel with Moist AirFUELCH 4 , O 2 , H 2 ,N 2 , CO 2AIR20°C, φ = 80%Combustionchamber1 atmFIGURE 15–12Schematic for Example 15–3.CO 2H 2 ON 2A certain natural gas has the following volumetric analysis: 72 percent CH 4 ,9 percent H 2 , 14 percent N 2 , 2 percent O 2 , and 3 percent CO 2 . This gas isnow burned with the stoichiometric amount of air that enters the combustionchamber at 20°C, 1 atm, and 80 percent relative humidity, as shown inFig. 15–12. Assuming complete combustion and a total pressure of 1 atm,determine the dew-point temperature of the products.Solution A gaseous fuel is burned with the stoichiometric amount of moistair. The dew point temperature of the products is to be determined.