Q.3) In Table 1, some physical properties of superheated water are given with respect to temperature....

 

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Q.3) In Table 1, some physical properties of superheated water are given with respect to temperature. Please find the value of internal energy, u, of superheated water at 216°C by using (a) second-order Newton's interpolating interpolating polynomial of the second order and (c) linear interpolation. Compare the results (40 Points) polynomial, (b) Lagrange h °C m3/kg kJ/kg kJ/kg kJ/kg-K P = 0.10 MPa (99.61°C) Sat. 1.6941 2505.6 2675.0 7.3589 50 100 150 1.9367 2582.9 2776.6 7.6148 1.6959 2506.2 2675.8 7.3611 200 2.1724 2658.2 2875.5 7.8356 250 2.4062 2733.9 2974.5 8.0346 300 2.6389 2810.7 3074.5 8.2172 400 3.1027 2968.3 3278.6 8.5452 500 3.5655 3132.2 3488.7 8.8362 600 4.0279 3302.8 3705.6 9.0999 700 4.4900 3480.4 3929.4 9.3424 800 4.9519 3665.0 4160.2 9.5682 900 5.4137 3856.7 4398.0 9.7800 1000 5.8755 4055.0 4642.6 9.9800 1100 6.3372 4259.8 4893.6 10.1698 1200 6.7988 4470.7 5150.6 10.3504 1300 7.2605 4687.2 5413.3 10.5229 Table 1. Q.3) In Table 1, some physical properties of superheated water are given with respect to temperature. Please find the value of internal energy, u, of superheated water at 216°C by using (a) second-order Newton's interpolating interpolating polynomial of the second order and (c) linear interpolation. Compare the results (40 Points) polynomial, (b) Lagrange h °C m3/kg kJ/kg kJ/kg kJ/kg-K P = 0.10 MPa (99.61°C) Sat. 1.6941 2505.6 2675.0 7.3589 50 100 150 1.9367 2582.9 2776.6 7.6148 1.6959 2506.2 2675.8 7.3611 200 2.1724 2658.2 2875.5 7.8356 250 2.4062 2733.9 2974.5 8.0346 300 2.6389 2810.7 3074.5 8.2172 400 3.1027 2968.3 3278.6 8.5452 500 3.5655 3132.2 3488.7 8.8362 600 4.0279 3302.8 3705.6 9.0999 700 4.4900 3480.4 3929.4 9.3424 800 4.9519 3665.0 4160.2 9.5682 900 5.4137 3856.7 4398.0 9.7800 1000 5.8755 4055.0 4642.6 9.9800 1100 6.3372 4259.8 4893.6 10.1698 1200 6.7988 4470.7 5150.6 10.3504 1300 7.2605 4687.2 5413.3 10.5229 Table 1.