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# P mi ui x u i u y i ui 26 m m i where u is the total

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Unformatted text preview: ion of the species. P mi ui X U i u¼ ¼ ¼ y i ui ; (2.6) m m i where U is the total internal energy of the mixture and ui is the internal energy per mass of species i. Similarly, enthalpy per unit mass of mixture is X h¼ y i hi i and speciﬁc heat at constant pressure per unit mass of mixture is cp ¼ X yi cp;i : i A molar base property, often denoted with a ^ over bar, is determined by the sum of the species property per mole for each species weighted by the species mole fraction, such as internal energy per mole of mixture X ^ ^ u¼ x i ui ; i enthalpy per mole of mixture ^ h¼ X i ^ x i hi ; 2.2 Combustion Stoichiometry 17 and entropy per mole of mixture ^ s¼ X ^ xi si : i Assuming constant speciﬁc heats during a thermodynamic process, changes of energy, enthalpy, and entropy of an individual species per unit mass are described as follows: Dui ¼ cv;i ðT2 À T1 Þ (2.7) Dhi ¼ cp;i ðT2 À T1 Þ (2.8) Dsi ¼ cp;i ln T2 Pi;2 À Ri ln T1 Pi;1 (2.9) Pi,1 and Pi,2 denote the partial pressures of species i at state 1 and state 2, respectively. ^ Ri is the gas constant for species i (Ri ¼ Ru =Mi ¼ universal gas constant/molecular mass of species i). The overall change of entropy for a combustion system is DS ¼ X mi Dsi : i A summary of the thermodynamic properties of mixtures is provided at the end of the chapter. 2.2 Combustion Stoichiometry For a given combustion device, say a piston engine, how much fuel and air should be injected in order to completely burn both? This question can be answered by balancing the combustion reaction equation for a particular fuel. A stoichiometric mixture contains the exact amount of fuel and oxidizer such that after combustion is completed, all the fuel and oxidizer are consumed to form products. This ideal mixture approximately yields the maximum ﬂame temperature, as all the energy released from combustion is used to heat the products. For example, the following reaction equation can be written for balancing methane-air combu...
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## This document was uploaded on 01/20/2014.

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