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 1.3 1.4 1.5 CP (kJ/kg.K) 1.1410 1.1573 1.1722 1.1858 1.1982 1.2095 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?

numerical analysis

Answer 1

Ans; Given that The constant pressure specific heat of air at different temperatures are in below table cp CkJ lleg. 10) olun TO) 1.573 12 1.722 1:3 1.4 ।.858 l.uz 1 • 2005 (a) To Find op at Tal-usle Tulaule The cubic interpolation can be determine y cao = { ucaly (ni) tha) 120 y (nl=Loba) y roj thonych othen) y last Lg (nly (2) Licn) =3 n-ni in ning Now To consider the closer point, T=bus in T = 12,1-5, 1.4, 1.5 1.858,1•19821-2095 - 117221 sp

LOCT) TT EITT; To-TI To Tg To-T Loll-45) = 11:45 .45-lu 1-48-ins (2-1-3 12-1.4 1-2-1-3 = 0.0625 2 (T) = (1-us-12) L' =-0.3125 1-45-1.4 1-3-1-4 1-3-1.5 ) les to be us - L (T) = 1.45-1-2 4-45-1-3 -0.9378 1.4-1.2 1-5-1-4 L3 (T) =11:45-12 us-1-9 30-3125 1. Galo 105-1-3 The General formularis epit) - 66) epo tdct).cp, +6 (0348, +41 (HDCE = 0.0625 (1-1722)+(00-3125) 0.1888 170-9375 (1-1981)+0.3125 C1-2018) 1.20398 Now to wowhe Talous kid <p =1:20193 ~ 1-204 (6) for suppous fonolfistinad -forn) be the (+1) values of the fonction y = f(n) caresponding to the orginents n = noinic an. weuera the first differnue is given by

f(n)-f(no) The abow divided differenca equation is f(none) = na-no fon,,2) Mo and the second divided difference is given by f610, may m) - fonou) Independen Independeur of the order of argements Now to write ton) = fong) + (-ro) f (noinJ+ (no-us) (x-2) f(noinine) tch-ro)(x-x;)--(4-74-7) + Gronin...) To Derive the polynomial equation by the data croots tul that san find the critical points the deservication values. for each point nito wich root does newton's method common is within to convergeur to a root in the sensitivity of den developed model-