Chemical Engineering

05.02.6 Chapter 05.02yx 0, y 0x 1, y 1f 3 x , y 3 3xx2 , y 2xFigure 4 Cubic interpolation.Since we want to find the specific heat at T 61C, and we are using a third orderpolynomial, we need to choose the four data points closest to T 61Cthat also bracketT 61C to evaluate it. The four points are T0 42,T1 52, T2 82 and T3 100.(Choosing the four points as T0 22, T 142 , T 52 2and T3 82 is equally valid.)ThenT0 42,CpT04179T1 52,CpT14186T2 82,CpT24199T3 100,CpT34217gives2342 a a 42 a 42 a 42C p 0 1 2 3 417923C p52a0 a152a252 a352 418623C p82a0 a182a282 a382 419923100a a 100a 100 a 100 4217C p0 123Writing the four equations in matrix form, we have4142 1764 7.408810a0 41795 152 2704 1.406110a1 418651 82 6724 5.5137 10a 419926 1100 10000 10a3 4217Solving the above four equations gives