Tp k 2000 k 2500 k hptp mj 24183 7269 1885614

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Unformatted text preview: Þ rxn Pi Tp ¼ T0 þ ^ Ni;p cp;i i ð241:88 þ 0ÞkJ=mol ð0:047 þ 1:88 Á 0:035Þ kJ/mol À K $ 2;148 K ¼ 300 þ The average temperature of the products and reactants is now (2,148 K + 298 K)/ 2 ~ 1,223 K, indicating that the initial assumption of Tave ¼ 1,500 K was too high. Using the new average temperature of 1,223 K to evaluate the specific heats, the calculated flame temperature becomes Tp ~ 2,253 K. The average temperature is now Tave ¼ 1,275 K. This new average temperature can be used to calculate the specific heats and the process should be continued until the change in the average temperature is on the order of 20 K. By doing this procedure, we obtain TP ~ 2,230 K. Method 2: Iterative enthalpy balance: X ^ Ni;p Dho;p þ i i X HP ðTP Þ ¼ HR ðTR Þ X X ^ ^ ^ Ni;p hsi;p ðTp Þ ¼ Ni;R Dho;R þ Ni;R hsi;R ðTR Þ i i i i ^ ^ ^ ^ NH2 O Dho 2 O þ NH2 O hs;H2 O ðTP Þ þ NN2 Dho 2 þ NN2 hs;N2 ðTP Þ H N ^ ^ ^ ^ ¼ NH Dho þ NH hs;H ðTR Þ þ NO Dho þ NO hs;O ðTR Þ 2 H2 2 2 2 O2 2 2 ^ ^ þ NN2 Dho 2 þ NN2 hs;N2 ðTR Þ N ^ ^ ^ 1 Á Dh0 2 O þ hs;H2 O ðTP Þ þ 0 þ 1:88 Á hs;N2 ðTP Þ ¼ 0 þ 0 þ 0 þ 0 þ 0 þ 0 H ^ ^ ^ Dh0 2 O þ hs;H2 O ðTP Þ þ 1:88 Á hs;N2 ðTP Þ ¼ 0: H The first step is to guess the product temperature. For this case, let’s pick TP ¼ 2,000 K. We now plug in the value for the heat of formation of water and use thermodynamic property tables to evaluate the sensible enthalpy terms. TP (K) 2,000 K 2,500 K HP(TP) (MJ) À241.83 + 72.69 + 1.88·56.14 ¼ À63.6 MJ À241.83 + 98.96 + 1.88·74.31 ¼ À3.1 MJ 38 2 Thermodynamics of Combustion Our initial guess of TP ¼ 2,000 K was too low. The process was repeated with a higher guess of TP ¼ 2,500 K which resulted in a much smaller remainder, implying that TP ~ 2,500 K. For more accuracy, we can use linear extrapolation (or interpolation if we bracketed the real value): TP À 2; 500 0 þ 3: 1 ¼ 2;500 À 2;000 À3:1 þ 63:6 TP ¼ 2;526K Method 3: Cantera. Assume H2, O2, and H2O are the only species in the system; equilibrium tem...
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This document was uploaded on 01/20/2014.

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