Thermodynamics

Chapter 15 | 769The h – f ° of liquid propane is obtained by subtracting the h– fg of propane at25°C from the h – f ° of gas propane. Substituting givesQ out 11 kmol C 3 H 8 231118,910 h 298 h 298 2 kJ>kmol C 3 H 8 4 17.5 kmol O 2 2310 8150 86822 kJ>kmol O 2 4 128.2 kmol N 2 2310 8141 86692 kJ>kmol N 2 4 12.7 kmol CO 2 231393,520 71,078 93642 kJ>kmol CO 2 4 10.3 kmol CO231110,530 47,517 86692 kJ>kmol CO4 14 kmol H 2 O231241,820 57,999 99042 kJ>kmol H 2 O4 12.65 kmol O 2 2310 49,292 86822 kJ>kmol O 2 4 128.2 kmol N 2 2310 47,073 86692 kJ>kmol N 2 4 363,880 kJ>kmol of C 3 H 8Thus 363,880 kJ of heat is transferred from the combustion chamber foreach kmol (44 kg) of propane. This corresponds to 363,880/44 8270 kJof heat loss per kilogram of propane. Then the rate of heat transfer for amass flow rate of 0.05 kg/min for the propane becomesQ # out m # q out 10.05 kg>min218270 kJ>kg2 413.5 kJ>min 6.89 kWEXAMPLE 15–7First-Law Analysis of Combustion in a BombThe constant-volume tank shown in Fig. 15–24 contains 1 lbmol of methane(CH 4 ) gas and 3 lbmol of O 2 at 77°F and 1 atm. The contents of the tankare ignited, and the methane gas burns completely. If the final temperatureis 1800 R, determine (a) the final pressure in the tank and (b) the heattransfer during this process.Solution Methane is burned in a rigid tank. The final pressure in the tankand the heat transfer are to be determined.Assumptions 1 The fuel is burned completely and thus all the carbon in thefuel burns to CO 2 and all the hydrogen to H 2 O. 2 The fuel, the air, and thecombustion gases are ideal gases. 3 Kinetic and potential energies are negligible.4 There are no work interactions involved.Analysis The balanced combustion equation isBEFOREAFTERREACTIONREACTIONCO 21 lbmol CH 4 H 2 O3 lbmol O 2 O 277°F1800 R1 atmP 2FIGURE 15–24Schematic for Example 15–7.(a) At 1800 R, water exists in the gas phase. Using the ideal-gas relation forboth the reactants and the products, the final pressure in the tank is determinedto beSubstituting, we getCH 4 1g2 3O 2 S CO 2 2H 2 O O 2P react V N react R u T reactP prod V N prod R u T prodfP prod P react a N prodN reactba T prodT reactbP prod 11 atm2a 4 lbmol4 lbmol ba1800 R b 3.35 atm537 R