Chapter8_A - Chapter 8 - Section A - Mathcad Solutions 8.1...

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For isentropic expansion, S' 3 S 2 := x' 3 S' 3 S liq S lv := x' 3 0.855 = H' 3 H liq x' 3 H lv + := H' 3 2246 = η turbine H 3 H 2 H' 3 H 2 := η turbine 0.805 = Ans. W s H 3 H 2 := Q H H 2 H 1 := W s 1.035 10 3 × = Q H 3.322 10 3 × = η cycle W s Q H := η cycle 0.311 = Ans. Chapter 8 - Section A - Mathcad Solutions 8.1 With reference to Fig. 8.1, SI units, At point 2: Table F.2, H 2 3531.5 := S 2 6.9636 := At point 4: Table F.1, H 4 209.3 := At point 1: H 1 H 4 := At point 3: Table F.1, H liq H 4 := H lv 2382.9 := x 3 0.96 := H 3 H liq x 3 H lv + := H 3 2496.9 = S liq 0.7035 := S lv 7.3241 := 266
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(c) The rate of heat addition, Step 1--2: Qdot12 mdot H2 H1 () := Qdot12 1.931 10 3 × = (kJ/s) (d) The rate of heat rejection, Step 3--4: H3 Hliq x3 Hvap Hliq + := H4 Hliq x4 Hvap Hliq + := H4 699.083 = H3 1.919 10 3 × = Qdot34 mdot H4 H3 := Qdot34 1.22 10 3 × = (kJ/s) (e) Wdot12 0 := Wdot34 0 := Wdot23 mdot H3 H2 := Wdot23 873.222 = Wdot41 mdot H1 H4 := Wdot41 161.617 = (f) η Wdot23 Wdot41 + Qdot12 := η 0.368 = Note that the first law is satisfied: Σ Q Qdot12 Qdot34 + := Σ W Wdot23 Wdot41 + := Σ Q Σ W + 0 = 8.2 mdot 1.0 := (kg/s) The following property values are found by linear interpolation in Table F.1: State 1, Sat. Liquid at TH: H1 860.7 := S1 2.3482 := P1 3.533 := State 2, Sat. Vapor at TH: H2 2792.0 := S2 6.4139 := P2 3.533 := State 3, Wet Vapor at TC: Hliq 112.5 := Hvap 2550.6 := P3 1616.0 := State 4, Wet Vapor at TC: Sliq 0.3929 := Svap 8.5200 := P4 1616.0 := (a) The pressures in kPa appear above. (b) Steps 2--3 and 4--1 (Fig. 8.2) are isentropic, for which S3=S2 and S1=S4. Thus by Eq. 6.82): x3 S2 Sliq Svap Sliq := x3 0.741 = x4 S1 Sliq Svap Sliq := x4 0.241 = 267
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8.3 The following vectors contain values for Parts (a) through (f). Enthalpies and entropies for superheated vapor, Tables F.2 and F.4 @ P2 and T2 (see Fig. 8.4): H 2 3622.7 kJ kg 3529.6 kJ kg 3635.4 kJ kg 3475.6 kJ kg 1507.0 BTU lb m 1558.8 BTU lb m := S 2 6.9013 kJ kg K 6.9485 kJ kg K 6.9875 kJ kg K 6.9145 kJ kg K 1.6595 BTU lb m rankine 1.6759 BTU lb m rankine := Sat. liq. and sat. vap. values from Tables F.2 and F.4 @ P3 = P4: H liq 191.832 kJ kg 251.453 kJ kg 191.832 kJ kg 419.064 kJ kg 180.17 BTU lb m 69.73 BTU lb m := H vap 2584.8 kJ kg 2609.9 kJ kg 2584.8 kJ kg 2676.0 kJ kg 1150.5 BTU lb m 1105.8 BTU lb m := 268
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S liq 0.6493 kJ kg K 0.8321 kJ kg K 0.6493 kJ kg K 1.3069 kJ kg K 0.3121 BTU lb m rankine 0.1326 BTU lb m rankine := S vap 8.1511 kJ kg K 7.9094 kJ kg K 8.1511 kJ kg K 7.3554 kJ kg K 1.7568 BTU lb m rankine 1.9781 BTU lb m rankine := V liq 1.010 cm 3 gm 1.017 cm 3
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Chapter8_A - Chapter 8 - Section A - Mathcad Solutions 8.1...

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