Thermodynamics

770 | Thermodynamics(b) Noting that the process involves no work interactions, the heat transferduring this constant-volume combustion process can be determined from theenergy balance E in E out E system applied to the tank,Q out a N p 1h° f h h° Pv 2 p a N r 1h° f h h° Pv 2 rSince both the reactants and the products are assumed to be ideal gases, allthe internal energy and enthalpies depend on temperature only, and the Pv –terms in this equation can be replaced by R u T. It yieldsQ out a N r 1h° f R u T2 r a N p 1h° f h 1800 R h 537 R R u T2 psince the reactants are at the standard reference temperature of 537 R.From h – f ° and ideal-gas tables in the Appendix,h – f° h – 537 R h – 1800 RSubstance Btu/lbmol Btu/lbmol Btu/lbmolCH 4 32,210 — —O 2 0 3725.1 13,485.8CO 2 169,300 4027.5 18,391.5H 2 O(g) 104,040 4258.0 15,433.0Substituting, we haveQ out 11 lbmol CH 4 23132,210 1.986 5372 Btu>lbmol CH 4 4 13 lbmol O 2 2310 1.986 5372 Btu>lbmol O 2 4 11 lbmol CO 2 231169,300 18,391.5 4027.5 1.986 18002Btu>lbmol CO 2 4 12 lbmol H 2 O231104,040 15,433.0 4258.0 1.986 18002Btu>lbmol H 2 O4 11 lbmol O 2 2310 13,485.8 3725.1 1.986 18002 Btu>lbmol O 2 4 308,730 Btu/lbmol CH 4Discussion On a mass basis, the heat transfer from the tank would be308,730/16 19,300 Btu/lbm of methane.InsulationFuelAirFIGURE 15–25CombustionchamberProductsT maxThe temperature of a combustionchamber becomes maximum whencombustion is complete and no heatis lost to the surroundings (Q 0).15–5 ADIABATIC FLAME TEMPERATUREIn the absence of any work interactions and any changes in kinetic or potentialenergies, the chemical energy released during a combustion processeither is lost as heat to the surroundings or is used internally to raise thetemperature of the combustion products. The smaller the heat loss, thelarger the temperature rise. In the limiting case of no heat loss to the surroundings(Q 0), the temperature of the products reaches a maximum,which is called the adiabatic flame or adiabatic combustion temperatureof the reaction (Fig. 15–25).