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Question 7.3: Problem: Find the specific enthalpy of a saturated water‐ste...

Problem: Find the specific enthalpy of a saturated water‐steam mixture with 40% quality at a temperature of 50 °C.

Find: Specific enthalpy h.

Known: The water‐steam mixture is at the saturation temperature T_{sat} = 50 °C, quality x = 0.4.

Governing Equation:

Mixture property (y)                      y=xy_g + (1-x)y_f

Properties: From Table 7.2 at T_{sat} = 50 °C, enthalpy of liquid h_f = 209.33 kJ / kg and vapour h_g = 2592.1 kJ / kg.

Table 7.2 Properties of saturated water as a function of temperature.

Temp. (°C) Pressure (MPa) Spec. Vol. (m³/kg) Int. Energy (kJ/kg) Enthalpy (kJ/kg) Entropy (kJ/kgK)
T_{sat} P v_f v_g u_f u_g h_f h_g s_f s_g
0.01 0.000 611 3 0.001 000 206.14 0.00 2375.3 0.00 2501.4 0.0000 9.1562
5 0.000 872 1 0.001 000 147.12 20.97 2382.3 20.98 2510.6 0.0761 9.0257
10 0.001 227 6 0.001 000 106.38 42.00 2389.2 42.01 2519.8 0.1510 8.9008
15 0.001 705 1 0.001 001 77.93 62.99 2396.1 62.99 2528.9 0.2245 8.7814
20 0.002 339 0.001 002 57.79 83.95 2402.9 83.96 2538.1 0.2966 8.6672
25 0.003 169 0.001 003 43.36 104.88 2409.8 104.89 2547.2 0.3674 8.5580
30 0.004 246 0.001 004 32.89 125.78 2416.6 125.79 2556.3 0.4369 8.4533
35 0.005 628 0.001 006 25.22 146.67 2423.4 146.68 2565.3 0.5053 8.3531
40 0.007 384 0.001 008 19.52 167.56 2430.1 167.57 2574.3 0.5725 8.2570
45 0.009 593 0.001 010 15.26 188.44 2436.8 188.45 2583.2 0.6387 8.1648
50 0.012 349 0.001 012 12.03 209.32 2443.5 209.33 2592.1 0.7038 8.0763
55 0.015 758 0.001 015 9.568 230.21 2450.1 230.23 2600.9 0.7679 7.9913
60 0.019 940 0.001 017 7.671 251.11 2456.6 251.13 2609.6 0.8312 7.9096
65 0.025 03 0.001 020 6.197 272.02 2463.1 272.06 2618.3 0.8935 7.8310
70 0.031 19 0.001 023 5.042 292.95 2469.6 292.98 2626.8 0.9549 7.7553
75 0.038 58 0.001 026 4.131 313.90 2475.9 313.93 2643.7 1.0155 7.6824
80 0.047 39 0.001 029 3.407 334.86 2482.2 334.91 2635.3 1.0753 7.6122
85 0.057 83 0.001 033 2.828 355.84 2488.4 355.90 2651.9 1.1343 7.5445
90 0.070 14 0.001 036 2.361 376.85 2494.5 376.92 2660.1 1.1925 7.4791
95 0.084 55 0.001 040 1.982 397.88 2500.6 397.96 2668.1 1.2500 7.4159
100 0.101 35 0.001 044 1.6729 418.94 2506.5 419.04 2676.1 1.3069 7.3549
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h=xh_g+(1-x) h_f =0.4 \times 2592.1 \ kJ/kg + (1-0.4)\times 209.33 \ kJ/kg=1162.438 \ kJ/kg

Answer: The mixture enthalpy is 1162.4 kJ / kg.

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