Determine the total apparent specific heat at constant pressure (c_p,mix in kJ/kg · K) for a fuel–air reactant mixture containing 1 kmol CH₄, 2.5 kmol O₂, and 9.4 kmol N₂ at 500 K and 1 atm. Use specific heat values for each species from Table E.1.

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TABLE E.1 Critical Constants and Specific Heats for Selected Gases* P. (105 Pa) 62.4 37.7 Substance Acetylene (C₂H₂) Air (equivalent) Ammonia (NH3) Benzene (CH) n-Butane (C4H10) Carbon dioxide (CO₂) Carbon monoxide (CO) * Refrigerant 134a (C₂F4H₂) Ethane (C₂Hg) Ethylene (C₂H4) Helium (He) m (kg/kmol) 26.04 28.97 17.04 78.11 58.12 44.01 28.01 102.03 30.07 28.05 4.003 2.016 Tc (K) 309 133 406 562 425.2 304.2 133 374.3 305.4 283 5.2 33.2 190.7 126.2 154.4 370 431 647.1 112.8 48.3 37.9 73.9 35.0 40.6 48.8 51.2 2.3 13.0 46.4 33.9 50.5 42.5 78.7 220.6 vc (m³/kmol) 0.112 0.0829 0.0723 0.256 0.257 0.0941 0.0928 0.200 0.148 0.128 0.0579 cy (kJ/kg-K) 1.37 0.718 0.242 1.66 0.274 0.67 0.274 1.56 0.276 0.657 0.294 0.744 0.262 0.76 0.285 1.48 Zc 0.272 0.284 0.279 1.23 0.300 3.12 Hydrogen (H₂) 0.0648 Methane (CH₂) 16.04 0.0991 Nitrogen (N₂) 28.01 0.0897 Oxygen (0₂) 32.00 0.0741 Propane (C3H8) 44.09 0.200 Sulfur dioxide (SO₂) 64.06 0.124 Water (H₂O) 18.02 0.0558 Adapted from Wark, K, Jr., and Richards, D. E., Thermodynamics, 6th edn, McGraw-Hill, New York, 1999. 0.304 0.290 0.291 0.290 10.2 1.70 0.743 0.658 0.278 1.48 0.268 0.471 0.230 1.40 Cp (kJ/kg-K) 1.69 1.005 2.15 0.775 1.71 0.846 1.04 0.85 1.75 1.53 5.19 14.3 2.22 1.04 0.918 1.67 0.601 1.86