# Example 5.1 m0 = 1100.0 kg KE = 400.0 kJ V0 = sqrt(2 * KE / m0) ; m/s PE = KE ; kJ H0 = PE / m0 /grav() ; m # Example 5.1E m0 = 2400.0 lbm KE = 400.0 Btu V0 = sqrt(2 * KE / m0) ; ft/s PE = KE ; Btu H0 = PE / m0 / grav() ; ft # Example 5.2 W12 = -5090.0 kJ Q12 = -1500.0 kJ delU = Q12 - W12 ; kJ # Example 5.3 ms0 = 10.0 kg mw = 100.0 kg hs = 10.2 m Us = ms0 * grav() * hs; kJ # Example 5.4a T0 = 300.0 degC u0 = 2780.0 kJ/kg ug = 2563.0 kJ / kg Pg = 8581.0 kPa u1 = 2781.0 kJ / kg P1 = 1600.0 kPa u2 = 2776.8 kJ / kg P2 = 1800.0 kPa Pinterpolated = P1 + (u0 - u1) * (P2 - P1) / (u2 - u1) ; kPa # Example 5.4b P0 = 2000.0 kPa u0 = 2000.0 kJ/kg uf = 906.4 kJ / kg ug = 2600.3 kJ / kg Tg = 212.4 degC T0 = Tg ufg = 1693.8 kJ / kg x0 = (u0 - uf) / ufg nf = 0.0011770 m^3/kg nfg = 0.098450 m^3/kg n0 = nf + x0 * nfg ; m^3/kg # Example 5.5 Vv = 5.0 m^3 Vliq = 0.05 m^3 Vvap = Vv - Vliq ; m^3 Pvap = 0.1 Mpa nf = 0.0010430 m^3/kg u1_liq = 417.360 kJ/kg ng = 1.6940 m^3/kg u1_vap = 2506.1 kJ/kg m1_liq = Vliq / nf ; kg m1_vap = Vvap / ng ; kg U1 = m1_liq * u1_liq + m1_vap * u1_vap ; kJ m0 = m1_liq + m1_vap ; kg n2 = Vv / m0 ; m^3/kg Pg = 2.03 Mpa P2 = Pg ng2 = 0.0098 m^3/kg u2 = 2600.5000 kJ / kg U2 = m0 * u2 ; kJ Q12 = U2 - U1 ; kJ # Example 5.5E Vv = 100.0 ft^3 Vliq = 1.0 ft^3 Vvap = Vv - Vliq ; ft^3 Pvap = 14.7 psi nf = 0.0167200 ft^3/lbm u1_liq = 180.100 Btu/lbm ng = 26.8000 ft^3/lbm u1_vap = 1077.6 Btu/lbm m1_liq = Vliq / nf ; lbm m1_vap = Vvap / ng ; lbm U1 = m1_liq * u1_liq + m1_vap * u1_vap ; Btu m0 = m1_liq + m1_vap ; lbm n2 = Vv / m0 ; ft^3/lbm Pg = 294.00 psi P2 = Pg ng2 = 1.5750 ft^3/lbm u2 = 1117.0000 Btu/lbm U2 = m0 * u2 ; Btu Q12 = U2 - U1 ; Btu # Example 5.6 V1 = 0.1 m^3 m0 = 0.5 kg P0 = 0.4 Mpa T0 = 300.0 degC n1 = V1 / m0 ; m^3 / kg nf = 0.0010840 m^3 / kg nfg = 0.4614000 m^3 / kg x1 = (n1 - nf) / nfg hf = 604.7400 kJ/kg hfg = 2133.8 kJ/kg h1 = hf + x1 * hfg ; kJ/kg h2 = 3066.8 kJ/kg Q12 = m0 * (h2 - h1) ; kJ n2 = 0.655 m^3 / kg W12 = m0 * P0 * (n2 - n1) ; kJ delU = Q12 - W12 ; kJ uf = 604.3100 kJ/kg ufg = 1949.3 kJ/kg u1 = uf + x1 * ufg ; kJ/kg u2 = 2804.8000 kJ/kg Q12 = delU + W12 ; kJ # Example 5.7 m0 = 1.0 kg T1 = 300.0 degK T2 = 1500.0 degK # Method 1: Ideal Gas Tables h1 = 273.2 kJ/kg h2 = 1540.2 kJ/kg Dh = h2 - h1 ; kJ/kg # Method 2: Integrated empiraical equation q1 = 0.3000 q2 = 1.5000 c0 = 0.8800 c1 = -0.0001 c2 = 0.5400 c3 = -0.330 Dh1 = 1e6 kJ/kg * (c0 * q1 + c1 * q1^2/2 + c2 * q1^3 / 3 + c3 * q1^4/ 4) ; kJ/kg Dh2 = 1e6 kJ/kg * (c0 * q2 + c1 * q2^2/2 + c2 * q2^3 / 3 + c3 * q2^4/ 4) ; kJ/kg Dh = Dh2 - Dh1 ; kJ/kg # Method 3: Assumed specific heat Cp0 = 0.922 kJ/kg/degK Dh = Cp0 * (T2 - T1) ; kJ/kg # Method 3: Assumed specific heat Cp0 = 1.077 kJ/kg/degK Dh = Cp0 * (T2 - T1) ; kJ/kg # Example 5.8 V1 = 0.1 m^3 P1 = 150.0 kPa T1 = 25.0 degC P2 = 1.0 Mpa T2 = 150.0 degC W12 = -20.0 kJ R = 0.29680 kJ/kg degK m0 = P1 * V1/ (R * T1) ; kg Cn0 = 0.7450 kJ / kg degK Q12 = m0 * Cn0 * (T2 - T1) + W12 ; kJ # Example 5.8E V1 = 2.0 ft^3 P1 = 20.0 psi T1 = 80.0 degF P2 = 160.0 psi T2 = 300.0 degF W12 = -9.2 Btu R = 55.15000 ft lbf / lbm degR m0 = P1 * V1/ (R * T1) ; lbm Cn0 = 0.1770 Btu / lbm degR Q12 = m0 * Cn0 * (T2 - T1) + W12 ; Btu # Example 5.9 i0 = 20.0 A V0 = 12.8 V Qdot = -10.0 W dUdt = Qdot + i0 * V0 ; J/s # Example 5.10 mstove = 25.0 kg mpine = 5.0 kg mair = 1.0 kg T1 = 20.0 degC P1 = 101.0 kPa Qdot = 1500.0 W degC T2 = 75.0 degC Cstove = 0.42 kJ/kg Cpine = 1.38 kJ/kg Cair = 0.717 kJ/kg Cstove * mstove + Cpine * mpine + Cair * mair ; kJ SumCM = Cstove * mstove + Cpine * mpine + Cair * mair dTdt = Qdot / SumCM ; degC/s Dt = (T2 - T1) / (dTdt) ; min # Homework Problems: TBD