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13-27 13-53 The volume fractions of components of a gas mixture are given. This mixture is heated while flowing through a tube at constant pressure. The heat transfer to the mixture per unit mass of the mixture is to be determined. Assumptions All gases will be modeled as ideal gases with constant specific heats. Properties The molar masses of O2, N2, CO2, and CH4 are 32.0, 28.0, 44.0, and 16.0 kg/kmol, respectively (Table A-1). The constant-pressure specific heats of these gases at room temperature are 0.918, 1.039, 0.846, and 2.2537 kJ/kgK, respectively (Table A-2a). Analysis We consider 100 kmol of this mixture. Noting that volume fractions are equal to the mole fractions, mass of each component are m O2 N O2 M O2 (30 kmol)(32 kg/kmol) 960 kg m N2 N N2 M N2 (40 kmol)(28 kg/kmol) 1120 kg m CO2 N CO2 M CO2 (10 kmol)(44 kg/kmol) 440 kg m CH4 N CH4 M CH4 (20 kmol)(16 kg/kmol) 320 kg The total mass is qin m m m O2 m N2 m CO2 m CH4 960 1120 440 320 2840 kg 150 kPa 20C 30% O2, 40% N2 10% CO2, 20% CH4 (by volume) 150 kPa 200C Then the mass fractions are mf O2 m O2 960 kg 0.3380 2840 kg mm mf N2 m N2 1120 kg 0.3944 2840 kg mm mf CO2 m CO2 440 kg 0.1549 2840 kg mm mf CH4 m CH4 320 kg 0.1127 mm 2840 kg The constant-pressure specific heat of the mixture is determined from c p mf O2 c p ,O2 mf N2 c p , N2 mf CO2 c p ,CO2 mf CH4 c p ,CH4 0.3380 0.918 0.3944 1.039 0.1549 0.846 0.1127 2.2537 1.1051 kJ/kg K An energy balance on the tube gives q in c p (T2 T1 ) (1.1051 kJ/kg K )(200 20) K 199 kJ/kg PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.