Question

The constant-pressure specific heat of air at different temperatures are tabulated in the following table: T(K) 1.0 1.1 1.2 CP (kJ/kg.K) 1.1410 1.1573 1.1722 1.1858 1.1982 1.2095 1.3 1.4 1.5 a) Use a third order interpolation polynomial to find Cp at T = 1.45 K. Show complete solution. b) If you want to develop a model that passes through all these data points using the Newton's difference method, explain briefly without calculations how you will do it. Also, how can you test the sensitivity of your developed model?

please answer b briefly

Answer 1

solution: to the deta, the following given According ali Given that la) let the third order interpolation palymail y = a +bx't cxerox? fit methad 128 least busso square 2 2 n и s s = وع E C Yiza-bas cz; in dzi) leat minine se pub CO, ds da JS db 25 de dd O- weret Eg = na +bEx + cEx?rd Ex² ت Exy aEx+bEx?+cEx3+ dezu Exy² = a&x²+bex²+cE29+dexs Exy GEX37 bexh+cEx5 +dex - "ni nc ng nay xay 3 We have, Exlexnens no X 8 ît U 11 9.55 12.375 16.2979 Exo = 29.5045 1:1410 11573 r. na 13 +1722 EX5 = 21.78375 -8.85394 Exy Ex²y = 11.30315 1.4 1. 1982

los 1.2095 Exky 14.6820 EX 6.2 2 Ey=7 =7.064 EX ² 9.55 {x3 = 12.375 E24 - 16.2979 these vales and y substitating in equ W,0,0 on We con solving these get -0.004338 b 0.01 G042 C 2.184,178 1.107305 d they third onder palynonial become? -0.004338 + x +2-1841782? +1.109305) 2 60.016042) y at n = 1.45 Ta 1.45 k 2 ) 6.45) =C P 0.009339 (-0.016042 3 y + 2.194178 (1-45" - 1:67305 (+45) there fore therefore, cp= 1.1988

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