Thermodynamics

Chapter 15 | 777EXAMPLE 15–10Second-Law Analysis of Adiabatic CombustionMethane (CH 4 ) gas enters a steady-flow adiabatic combustion chamber at25°C and 1 atm. It is burned with 50 percent excess air that also enters at25°C and 1 atm, as shown in Fig. 15–33. Assuming complete combustion,determine (a) the temperature of the products, (b) the entropy generation,and (c) the reversible work and exergy destruction. Assume that T 0 298 Kand the products leave the combustion chamber at 1 atm pressure.Solution Methane is burned with excess air in a steady-flow combustionchamber. The product temperature, entropy generated, reversible work, andexergy destroyed are to be determined.Assumptions 1 Steady-flow conditions exist during combustion. 2 Air andthe combustion gases are ideal gases. 3 Changes in kinetic and potentialenergies are negligible. 4 The combustion chamber is adiabatic and thusthere is no heat transfer. 5 Combustion is complete.Analysis (a) The balanced equation for the complete combustion processwith 50 percent excess air isCH 4 1g2 3 1O 2 3.76N 2 2 S CO 2 2H 2 O O 2 11.28N 2Under steady-flow conditions, the adiabatic flame temperature is determinedfrom H prod H react , which reduces toCH 425°C, 1 atmAIR25°C, 1 atmT 0 = 25°CAdiabaticcombustionchamberFIGURE 15–33Schematic for Example 15–10.CO 2H 2 OO 2N 2since all the reactants are at the standard reference state and h – f ° O for O 2and N 2 . Assuming ideal-gas behavior for air and for the products, the h – f ° andh values of various components at 298 K can be listed asSubstituting, we havewhich yieldsa N p 1h° f h h°2 p a N r h° f,r 1Nh° f 2 CH4h – f °h– 298 KSubstance kJ/kmol kJ/kmolCH 4 (g) 74,850 —O 2 0 8682N 2 0 8669H 2 O(g) 241,820 9904CO 2 393,520 936411 kmol CO 2 231393,520 h CO2 93642 kJ>kmol CO 2 4 12 kmol H 2 O231241,820 h H2 O 99042 kJ>kmol H 2 O4 111.28 kmol N 2 2310 h N2 86692 kJ>kmol N 2 4 11 kmol O 2 2310 h O2 86822 kJ>kmol O 2 4 11 kmol CH 4 2174,850 kJ>kmol CH 4 2h CO2 2h H2 O h O2 11.28h N2 937,950 kJBy trial and error, the temperature of the products is found to beT prod 1789 K