# Example 10.1 T0 = 25.0 degC Pi0 = 5.0 Mpa Ti = 40.0 degC mdoti = 5.0 kg/s W1 = 900.0 kW q1 = W1 / mdoti ; kJ/kg T1 = 100.0 degC T2 = 200.0 degC Pe = 5.0 Mpa Te = 180.0 degC hi = 172.0 kJ/kg si = 0.5705 kJ/kg/degK he = 765.2 kJ/kg se = 2.1341 kJ/kg/degK q2 = he - hi - q1 q2_not = q2 * (1 kg / s); kW wrev = T0 * (se - si) - (he - hi) \ + q1 * (1 - T0 / T1) + q2 * (1 - T0 / T2) ; kJ/kg # Example 10.2 T0 = 25.0 degC Pi0 = 100.0 kPa Ti = 25.0 degC Pe = 1.0 Mpa Te = 540.0 degK q = -50.0 kJ/kg hi = 386.1 kJ/kg si = 1.7395 kJ/kg/degK he = 544.7 kJ/kg se = 7.4664 kJ/kg/degK w = hi - he + q ; kJ/kg R = 0.2870 kJ/kg degK wrev = T0 * (se - si - R * ln(Pe / Pi0)) \ - (he - hi) + q * (1 - T0 / T0) ; kJ/kg i = wrev - w ; kJ/kg # Example 10.2E T0 = 80.0 degF Pi0 = 14.7 psi Ti = 80.0 degF Pe = 150.0 psi Te = 960.0 degR q = -22.0 Btu/lbm hi = 129.2 Btu/lbm si = 1.6405 Btu/lbm/degR he = 231.2 Btu/lbm se = 1.7803 Btu/lbm/degR w = hi - he + q ; Btu/lbm R = 0.0686 Btu/lbm/degR wrev = T0 * (se - si - R * ln(Pe / Pi0)) \ - (he - hi) + q* (1 - T0 / T0) ; Btu/lbm i = wrev - w ; Btu/lbm # Example 10.3 Va = 1.0 m^3 Vb = 1.0 m^3 T1 = 20.0 degC x1 = 0.5 u1 = 1243.5 kJ/kg v1 = 28.89 m^3/kg s1 = 4.4819 kJ/kg/degK m1 = Va / v1 ; kg v2 = (Va + Vb) * v1 / Va ; m^3/kg u2 = u1 ; kJ/kg T2 = 9.1 degC x2 = 0.513 s2 = 4.6440 kJ/kg/degK Wrev = T1 * m1 * (s2 - s1) ; kJ I12 = Wrev ; kJ ## Example 10.4 # V0 = 1.0 m^3 # P1 = 200.0 kPa # T1 = 20.0 degC # Ta = -10.0 degC # u1 = 1369.5 kJ/kg # v1 = 0.6995 m^3/kg # s1 = 5.9270 kJ/kg/degK # hi = 134.4 kJ/kg # si = 0.5408 kJ/kg/degK # m1 = V0 / v1 ; kg # x2 = 0.002863 # vf = 0.001534 m^3/kg # vfg = 0.041684 m^3/kg # v2 = vf + x2 * vfg ; m^3/kg # uf = 133.964000 kJ/kg # ufg = 1175.2570 kJ/kg # u2 = uf + x2 * ufg ; kJ/kg # m2 = V0 / v2 ; kg # e = (u2 - hi) / v2 - m1 * (u1 - hi) ; kJ # s2 = 0.576200 kJ/kg degK # S0 = m2 * s2 - m1 * s1 - m1 * si ; kJ/degK # ICV = T1 * S0 ; kJ # Example 10.5 P0 = 0.1 Mpa T0 = 25.0 degC mdot1 = 30.0 kg/s P1 = 3.0 Mpa T1 = 350.0 degC P2 = 0.5 Mpa mdot2 = 5.0 kg/s T2 = 200.0 degC P3 = 15.0 kPa x3 = 0.9 mdot3 = mdot1 - mdot2 ; kg/s s0 = 0.3674 kJ/kg/degK h0 = 104.9 kJ/kg s1 = 6.7428 kJ/kg/degK h1 = 3115.3 kJ/kg y1 = (h1 - h0) - T0 * (s1 - s0) ; kJ/kg s2 = 7.0592 kJ/kg/degK h2 = 2855.4 kJ/kg y2 = (h2 - h0) - T0 * (s2 - s0) ; kJ/kg s3 = 7.2831 kJ/kg/degK h3 = 2361.8 kJ/kg y3 = (h3 - h0) - T0 * (s3 - s0) ; kJ/kg W0 = mdot1 * y1 - mdot2 * y2 - mdot3 * y3 ; kW s20 = 6.7428 kJ/kg/degK sf2 = 1.8606 kJ/kg/degK sfg2 = 4.9606 kJ/kg/degK xs2 = (s20 - sf2) / sfg2 hf2 = 640.2000 kJ/kg hfg2 = 2108.5000 kJ/kg h20 = hf2 + xs2 * hfg2 ; kJ/kg s30 = 6.7428 kJ/kg/degK sf3 = 0.7549 kJ/kg/degK sfg3 = 7.2536 kJ/kg/degK xs3 = (s30 - sf3) / sfg3 hf3 = 225.9000 kJ/kg hfg3 = 2373.1000 kJ/kg h30 = hf3 + x3 * hfg3 ; kJ/kg Wdot = mdot1 * h1 - mdot2 * h2 - mdot3 * h3 ; kW Wdots = mdot1 * h1 - mdot2 * h20 - mdot3 * h30 ; kW hs = Wdots / Wdot h2nd_law = Wdots / W0 ## Example 10.6 # T0 = 25.0 degC # T1 = 1100.0 degC # T2 = 550.0 degC # P1 = 0.1 Mpa # P2 = 0.1 Mpa # n = 1.09 kJ/kg/degK # Pw1 = 0.8 Mpa # Tw1 = 150.0 degC # Pw2 = 0.8 Mpa # Tw2 = 250.0 degC # hw1 = 632.2 kJ/kg # hw2 = 2950.0 kJ/kg # mdotprod_over_mdotw = (hw2 - hw1) / n / (T1 - T2) # s1 = 1.8418 kJ/kg/degK # s2 = 7.0384 kJ/kg/degK # dely21 = (hw2 - hw1) - T0 * (s2 - s1) ; kJ/kg # s3 = 1.8418 kJ/kg/degK # s4 = 7.0384 kJ/kg/degK # X3 = mdotprod_over_mdotw * n * (T1 - T2 - T0 *ln(T1 / T2)) ; kJ/kg # h2ndlaw = dely21 / X3 # Idot_over_mdotw = dely21 + X3 ; kJ/kg # s2 - s1 ; kJ/kg/degK # Y1 = mdotprod_over_mdotw * (s4 - s3) # Y2 = -mdotprod_over_mdotw * n * ln(T1 / T2) ; kJ/kg/degK # I1 = T0 * (s2 - s1) # I2 = mdotprod_over_mdotw * (s4 - s3) # Idot_over_mdotw = I1 + I2 ; kJ/kg/degK # Example 10.7 P0 = 100.0 kPa T0 = 25.0 degC h0 = 104.9 kJ/kg s0 = 0.3687 kJ/kg/degK si = 0.5705 kJ/kg/degK se = 2.1341 kJ/kg/degK htot_i = 171.97 kJ/kg htot_e = 765.25 kJ/kg y1 = htot_i - h0 - T0 * (si - s0) ; kJ/kg y2 = htot_e - h0 - T0 * (se - s0) ; kJ/kg q1 = 180.00 kJ/kg T1 = 100.0 degC q2 = 413.28 kJ/kg T2 = 200.0 degC F1 = (1 - T0 / T1) * q1 ; kJ/kg F2 = (1 - T0 / T2) * q2 ; kJ/kg T0_sgen = F1 + F2 + y1 - y2 ; kJ/kg h = ( F1 + F2 - T0_sgen) / (F1 + F2) # Example 10.8 T0 = 25.0 degC Wdot = 500.0 W The = 1000.0 degK Tc = 500.0 degK Qdot = Wdot ; W Sdot = Qdot / The ; W/degK Fdotdestruct = T0 * Sdot ; W Fdotout = (1 - T0 / The) * Qdot ; W Sdot = Qdot * (1 / Tc - 1 / The ) ; W/degK Fdotc = (1 - T0 / Tc) * Qdot ; W # Homework Problems: TBD