# Example 14.1 MO2 = 12.50 kmol MN2 = 47.00 kmol Mair = 1.00 kmol AFmole = (MO2 + MN2) / Mair ; kmol / kmol mfuel = 28.97 kg/mol mair = 114.20 kg/mol AFth = (MO2 + MN2) * mfuel / Mair / mair ; kg / kg ## Example 14.2 # P = 0.10 Mpa # MCO2 = 8.00 kmol # MH2O = 9.00 kmol # MO2 = 12.50 kmol # MN2 = 94.00 kmol # M = MCO2 + MH2O + MO2 + MN2 ; kmol l # fCO2 = MCO2 / M # fH2O = MH2O / M # fO2 = MO2 / M # fN2 = MN2 / M # Pp = P * fH2O ; kPa # Example 14.2E P = 14.70 psi MCO2 = 8.00 kmol MH2O = 9.00 kmol MO2 = 12.50 kmol MN2 = 94.00 kmol M = MCO2 + MH2O + MO2 + MN2 ; kmol fCO2 = MCO2 / M fH2O = MH2O / M fO2 = MO2 / M fN2 = MN2 / M Pp = P * fH2O ; psi # Example 14.3 MH2 = 0.1400 kmol MCO = 0.2700 kmol MCH4 = 0.0300 kmol MO2 = 0.0060 kmol MN2 = 0.5090 kmol MCO2 = 0.0450 kmol MO2_air = 0.2590 kmol MH2O_out = 0.2000 kmol MN2_out = 1.4820 kmol Mfuel = MH2 + MCO + MCH4 + MO2 + MN2 + MCO2 ; kmol AFth = MO2_air* Mfuel / MH2O_out ; kmol Excess = 0.2000 Y = (1 + Excess) * AFth ; kmol WH2 = 2.0000 kg/kmol WCO = 28.0000 kg/kmol WCH4 = 16.0000 kg/kmol WO2 = 32.0000 kg/kmol WN2 = 28.0000 kg/kmol WCO2 = 44.0000 kg/kmol WN2_out = 28.9700 kg/kmol SumMW = MH2 * WH2 + MCO * WCO + MCH4 * WCH4 + MO2 * WO2 + MN2 * WN2 + MCO2 * WCO2 AFthW = MN2 * WN2 / SumMW ; kg/kg # Example 14.4 fCO2 = 0.1000 fO2 = 0.0237 fCO = 0.0053 fN2 = 0.8710 Sumf = fCO2 + fO2 + fCO + fN2 cCH4 = 0.1053 a = cCH4 cO2 = 0.2316 b = cO2 cN2 = 0.8710 c =cN2 cH2O = 0.1053 d = cH2O cN2 = 8.2700 AF = (cO2 + cN2) / cCH4 ; kmol / kmol WN2 = 28.9700 kg/kmol WCH4 = 16.0000 kg/kmol AFW = AF * WN2 / WCH4 ; kg/kg AFth = 9.5200 AFWth = AF * WN2 / WCH4 ; kg/kg AFWth / AFW # Example 14.5 fS = 0.0060 fH = 0.0570 fC = 0.7920 fO = 0.1000 fN = 0.0150 fAsh = 0.0300 sumf = fS + fH + fC + fO + fN + fAsh Excess = 0.3000 MWS = 32.0000 MWH = 2.0000 MWC = 12.0000 MWO = 32.0000 MWN = 28.0000 MAsh = 0.0300 MS = fS / MWS MH = fH / MWH MC = fC / MWC MO = fO / MWO MN0 = fN / MWN MNN = 7.7300 AF = MNN * (1 + 3.76) * 28.97/ 100 ; kg/kg AFth = AF * (1 + Excess) ; kg/kg # Example 14.6 hCH4 = -74873 kJ hCO2 = -393522 kJ hH2O = -285830 kJ Q = hCO2 + 2 * hH2O - hCH4 ; kJ ## Example 14.7 # Px = 3.50 Mpa # Tx = 300.00 degC # P0 = 0.10 Mpa # T0 = 25.00 degC # Mx = 18.015 g # hbarf0 = -241826.00 kJ/kmol # Tave = (Tx + T0) / 2 ; degC # q = Tave / 1000 ; degC # y1 = 1.79 kJ/kg/degK/mol # y2 = 0.107 kJ/kg/degK/mol / degC # y3 = 0.586 kJ/kg/degK/mol / degC^2 # y4 = -0.20 kJ/kg/degK/mol / degC^3 # Cp0 =( y1 + y2 * q + y3 * q^2 +y4 * q^3 ) ; kJ/kg/degK # Dhbar = Mx * Cp0 * (Tx - T0) ; kJ/kmol # hbarTP = hbarf0 + Dhbar ; kJ/kmol # h1 = 2978 kJ/kg # h10 = 105 kJ/kg # Dhbar = Mx * (h1 - h10) ; # hbarf0 = -285830.00 kJ mol /kmol # hbarTP = hbarf0 + Dhbar ; kJ/kmol # h1 = 2978 kJ/kg # h10 = 2547 kJ/kg # Dhbar = Mx * (h1 - h10) ; kJ mol /kmol # hbarf0 = -241826.00 kJ mol /kmol # hbarTP3 = hbarf0 + Dhbar ; kJ/kmol # R = 0.0083 kJ/kg degK # Tc = 647.3000 degK # Pc = 22.0900 MPa # delh12 = 9494 kJ/kmol # Pr2 = Px / Pc # Tr2 = Tx / Tc # delh22 = 0.21 * R * Tc # hbarTP = hbarf0 - delh22 + delh12 ; kJ/kmol # Example 14.8 T1 = 25.00 degC T2 = 900.00 degK F0 = 0.25 kg/s nCO2 = 8.00 hf0_CO2 = -393522 kJ/kmol DhCO2 = 28030 kJ/kmol nH2O = 9.00 hf0_H2O = -241826 kJ/kmol DhH2O = 21892 kJ/kmol nO2 = 37.50 hf0_O2 = 0 kJ/kmol DhO2 = 19249 kJ/kmol nN2 = 188.00 hf0_N2 = 0 kJ/kmol DhN2 = 18222 kJ/kmol Sumni = nCO2 * ( hf0_CO2 + DhCO2) + nH2O * (hf0_H2O + DhH2O) \ + nO2 * (hf0_O2 + DhO2) + nN2 * (hf0_N2 + DhN2) ; kJ/kmol C0 = 1.00 kJ/s D0 = 114.23 kg Wcv = C0 * D0 / F0 ; kJ/kmol h0 = -250105 kJ/kmol Q = Sumni + Wcv / (1 mol) - h0 ; kJ/kmol ## Example 14.8 # T1 = 77.00 degF # T2 = 1100.00 degF # F0 = 1.00 lbm/hr # nCO2 = 8.00 # hf0_CO2 = -169184 Btu/mol lbm # DhCO2 = 11291 Btu/mol lbm # nH2O = 9.00 # hf0_H2O = -103966 Btu/mol lbm # DhH2O = 8858 Btu/mol lbm # nO2 = 37.50 # hf0_O2 = 0 Btu/mol lbm # DhO2 = 7778 Btu/mol lbm # nN2 = 188.00 # hf0_N2 = 0 Btu/mol lbm # DhN2 = 7374 Btu/mol lbm # Sumni = nCO2 * ( hf0_CO2 + DhCO2) + nH2O * (hf0_H2O + DhH2O) \ # + nO2 * (hf0_O2 + DhO2) + nN2 * (hf0_N2 + DhN2) ; Btu/ lbm # C0 = 1.00 kJ/s # D0 = 114.23 kg # Wcv = C0 * D0 / F0 ; Btu/mol lbm # h0 = -107526 Btu/mol lbm # Q = Sumni + Wcv / (1 mol) - h0 ; Btu/mol lbm ## Example 14.9 # T1 = 25.00 degC # T2 = 600.00 degK # hf0_C2H2 = 52467 kJ # R = 8.3145 kJ/kg degK # RT41 = 9916 kJ # S1 = hf0_C2H2 - RT41 ; kJ # nCO2 = 2.00 # hf0_C2H2 = -393522 kJ # DhCO2 = 12899 kJ # x1 = nCO2 * (hf0_CO2 + DhCO2) ; kJ # nH2O = 2.00 # hf0_H2O = -241826 kJ # DhH2O = 10463 kJ # x2 = nH2O * (hf0_H2O + DhH2O) ; kJ # S2 = x1 + x2 - 4 R T2 ; kJ # Q = S2 - S1 ; kJ # Example 14.10 # liquid propane - liquid water nCO2 = 3.00 hf0_CO2 = -393522 kJ nH2O = 4.00 hf0_H2O = -285830 kJ nC3H8 = -1.00 hf0_C3H8 = -120216 kJ S1 = -2203670 kJ M0 = 44.097 kg S1 / M0 ; kJ/kg # liquid propane - gaseous water nCO2 = 3.00 hf0_CO2 = -393522 kJ nH2O = 4.00 hf0_H2O = -241826 kJ nC3H8 = -1.00 hf0_C3H8 = -120216 kJ S2 = -2027654 kJ M0 = 44.097 kg S2 / M0 ; kJ/kg # gaseous propane liquid water nCO2 = 3.00 hf0_CO2 = -393522 kJ nH2O = 4.00 hf0_H2O = -285830 kJ nC3H8 = -1.00 hf0_C3H8 = -103900 kJ S2 = -2219986 kJ M0 = 44.097 kg S2 / M0 ; kJ/kg # Gaseous propane - gaseous water nCO2 = 3.00 hf0_CO2 = -393522 kJ nH2O = 4.00 hf0_H2O = -241826 kJ nC3H8 = -1.00 hf0_C3H8 = -103900 kJ S2 = -2043970 kJ M0 = 44.097 kg S2 / M0 ; kJ/kg # Example 14.11 T1 = 500.00 degK T2 = 25.00 degC DT = T1 - T2 ; degK Cp = 2.10 kJ/kg degK nC3H8 = 44 kg/kmol hf0_C3H8 = -103900 kJ/kmol nO2 = 5.000 Dhf0_O2 = 6095 kJ/kmol hR500 = (hf0_C3H8 + Cp * nC3H8 * DT) + nO2 * Dhf0_O2 ; kJ/kmol nCO2 = 3.00 hf0_CO2 = -393522 kJ/kmol Dhf0_CO2 = 8297 kJ/kmol nH2O = 4.00 hf0_H2O = -241826 kJ/kmol Dhf0_H2O = 6896 kJ/kmol hP500 = nCO2 * (hf0_CO2 + Dhf0_CO2) + nH2O * (hf0_H2O + Dhf0_H2O) ; kJ/kmol hRP = hP500 - hR500 ; kJ/kmol hpRP = hRP / nC3H8 ; kJ/kg ## Example 14.12 # HR = -250105.00 kJ/kmol # T1 = 900.00 degK # nCO2 = 8.00 # hf0_CO2 = -393522 kJ/kmol # DhCO2 = 28030 kJ/kmol # nH2O = 9.00 # hf0_H2O = -241826 kJ/kmol # DhH2O = 21892 kJ/kmol # nO2 = 37.500 # Dh_O2 = 19249 kJ/kmol # nH2 = 188.000 # DhH2 = 18222 kJ/kmol # HP1 = nCO2 * (hf0_CO2 + DhCO2) + nH2O * (hf0_H2O + DhH2O) \ # + nO2 * DhO2 + nN2 * DhN2 ; kJ/kmol # T1 = 1000.00 degK # nCO2 = 8.00 # hf0_CO2 = -393522 kJ/kmol # DhCO2 = 33400 kJ/kmol # nH2O = 9.00 # hf0_H2O = -241826 kJ/kmol # DhH2O = 25956 kJ/kmol # nO2 = 37.500 # Dhf0_O2 = 22710 kJ/kmol # nH2 = 188.000 # DhH2 = 21461 kJ/kmol # HP2 = nCO2 * (hf0_CO2 + DhCO2) + nH2O * (hf0_H2O + DhH2O) \ # + nO2 * DhO2 + nN2 * DhN2 ; kJ/kmol # X1 = T1 ; degK # Y1 = HP1 ; kJ/kmol # X2 = T2 ; degK # 1000 degK # Y2 = HP2 ; kJ/kmol # X = T = 961.8 degK # Y = Y1 + (X - X1) * (Y2 - Y1) / (X2 - X1) ; kJ/kmol # HP0 = -250105 kJ/kmol # e = Y - HP0 ## Example 14.13 # nCO2 = 2.00 # hf0_CO2 = -393522 kJ/kmol # nH2O = 2.00 # hf0_H2O = -241826 kJ/kmol # nC2H4 = -1.00 # hf0_C2H4 = 52467 kJ/kmol # nO2 = -3.00 # hf0_O2 = 0 kJ/kmol # DH = nCO2 * hf0_CO2 + nH20 * hf0_H2O \ # + nC2H4 * hf0C2H4 + nO2 * hf0_O2 ; kJ/kmol # nCO2 = 2.00 # s0_CO2 = 213.7950 kJ/kmol # nH2O = 2.00 # s0_H2O = 188.8430 kJ/kmol # nC2H4 = -1.00 # s0_C2H4 = 219.3300 kJ/kmol # nO2 = -3.00 # s0_O2 = 205.1480 kJ/kmol # DS = nCO2 * s0_CO2 + nH20 * s0_H2O + nC2H4 * s0C2H4 \ # + nO2 * s0_O2 ; kJ/kmol # T0 = 25.00 degC # DG = DH + T0 * DS ; kJ/kmol # n0 = 28.054 kg/kmol # Wrev = DG / n0 = -47478.357 kJ/kg ## Example 14.14 # nCO2 = 2.00 # hf0_CO2 = -393522 kJ/kmol # DhCO2 = 0 kJ/kmol # nH2O = 2.00 # hf0_H2O = -241826 kJ/kmol # DhCO2 = 0 kJ/kmol # nO2 = 9.00 # DhO2 = 0 kJ/kmol # nN2 = 45.10 # DhN2 = 0 kJ/kmol # H0 = 52467 kJ/kmol # X = nCO2 * (hf0_CO2 + DhCO2) + nH2O * (hf0_H2O + DhH2O)+ nO2 * DhO2 + nN2 * DhN2 - H0 = -1323163 kJ/kmol # TX = 1016.00 degK # nC2H4 = 1.00 # sC2H4 = 219.330 kJ/kmol degK # nO2 = 12.00 # sO2 = 205.147 kJ/kmol degK # nN2 = 45.10 # sN2 = 191.610 kJ/kmol degK # SR = nC2H2 sC2H2 + nO2 sO2 + nN2 sN2 ; kJ/kmol degK # nCO2 = 2.00 # sCO2 = 270.194 kJ/kmol degK # nH2O = 2.00 # sH2O = 233.355 kJ/kmol degK # nO2 = 9.00 # sO2 = 244.135 kJ/kmol degK # nN2 = 45.10 # sN2 = 228.691 kJ/kmol degK # SP = nCO2 * sCO2 + nH2O * sH2O+ nO2 * sO2 + nN2 * sN2 ; kJ/kmol degK # DS = SP - SR ; kJ/kmol degK # T0 = 25.00 degC # I = T0 * DS ; kJ/kmol # n0 = 28.05 kg/kmol # I0 = I / n0 ; kJ/kg # y0 = 46851.00 kg/kmol # y = y0 - I0 ; kJ/kg # Example 14.15 T0 = 25.00 degC nC2H4 = 1.00 hf0_C2H4 = 52467 kJ/kmol nCO2 = -2.00 hf0_CO2 = -393522 kJ/kmol nH2O = -2.00 hf0_H2O = -241826 kJ/kmol nC2H4 = 1.00 SC2H4 = 253.104 kJ/kmol degK nO2 = 12.00 SO2 = 218.264 kJ/kmol degK nN2 = 45.10 SN2 = 193.714 kJ/kmol degK nCO2 = -2.00 SCO2 = 241.806 kJ/kmol degK nH2O = -2.00 SH2O = 216.845 kJ/kmol degK nO2 = -9.00 SO2 = 220.653 kJ/kmol degK nN2 = -45.10 SN2 = 193.714 kJ/kmol degK Wrev = 1332377.922 kJ/kmol n0 = 28.05 kg/kmol Wrev / n0 ; kJ/kg # Example 14.16 nH2O = 2.00 hf0_H2O = -285830 kJ/kmol nH2 = -2.00 hf0_H2 = 0 kJ/kmol nO2 = -1.00 hf0_O2 = 0 kJ/kmol DH = -571660 kJ/kmol nH2O = 2.00 sH2O = 69.950 kJ/kmol degK nH2 = -2.00 sH2 = 130.678 kJ/kmol degK nO2 = -1.000 sO2 = 205.1480 kJ/kmol degK Ds = -326.604 kJ/kmol degK T0 = 25.00 degC DG = DH - T0 * Ds ; kJ/kmol n = 4.00 C0 = 96485.00 E0 = - DG / n / C0 ## Example 14.17 # nO2 = 10.28 # nN2 = 3.76 * nO2 # T0 = 25.00 degC # Tf = 50.00 degC # Cp = 114.230 kJ/kg/degK # DhC8H8 = 2.23 * Cp * (Tf - T0) ; kJ/kmol # nC8H8 = 1.00 # hf0_C8H8 = -250105 kJ/kmol # DhC8H8 = 6368323 # MC8H8 = 0.00 kg # VC8H8 = 0.00 m/s # HC8H8 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # nO2 = 10 # hf0_O2 = 0 kJ/kmol # DhO2 = 3034 kJ/kmol # MO2 = 32.00 kg # VO2 = 100.00 m/s # HO2 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # nN2 = 39 # hf0_N2 = 0 kJ/kmol # DhN2 = 2971 kJ/kmol # MN2 = 28.02 kg # VN2 = 100.00 m/s # HN2 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # z = HC8H8 + HO2 + HN2 ; kJ/kmol # nCO2 = 8.00 # hf0_CO2 = -393522 kJ/kmol # DhCO2 = 38891 kJ/kmol # MCO2 = 44.01 kg # VCO2 = 150.00 m/s # HCO2 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # nH2O = 9.00 # hf0_H2O = -241826 kJ/kmol # DhH2O = 30147 kJ/kmol # MH2O = 18.02 kg # VH2O = 150.00 m/s # HH2O = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # nO2 = -2 # hf0_O2 = 0 kJ/kmol # DhO2 = 26218 kJ/kmol # MO2 = 32.00 kg # VO2 = 150.00 m/s # HO2 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # nN2 = 39 # hf0_N2 = 0 kJ/kmol # DhN2 = 24758 kJ/kmol # MN2 = 28.02 kg # VN2 = 150.00 m/s # HN2 = n * (hf0 + Dh + M * V2 / 2) ; kJ/kmol # HP + KEP = HCO2 + HH2O + HO2 + HN2 ; kJ/kmol # error = (HP + KEP) - (HR + KER) ; kJ/kmol # FAideal = Cp / 4.76 nO2 28.97 # Example 14.18 Mdot = 325000.00 kg/hr P = 12.50 MPa T0 = 200.00 degC Ps = 9.00 MPa Ts = 500.00 degC K = 81000.00 kW Mdotcoal = 26700.00 kg/hr C0 = 2529.00 kJ/kg Ccoal = 33250.00 kJ/kg hs = Mdot * C0 / Mdotcoal / Ccoal hth = K / Mdotcoal / Ccoal # Homework Problems: TBD