Answer Happy

1. The mass of water in air was measured at various temperatures at 100% humidity and the following data were obtained. i 1 2 3 4 5 6 T (°C) 0 10 20 30 40 50 mwater (g/kg of air) 10 16 30 56 102 108 (a) (i) Use Matlab to determine the coefficients of 2nd and 3rd polynomials which fit the data best. Write down the equations for both polynomials. [4 marks] (ii) Plot the polynomials and the actual data points on one figure using Matlab. [3 marks] (iii) Determine the error for each polynomial. [2 marks] (b) Use the polynomial from part (a) which best fits the data to determine an estimate the amount of water in air at 45°C. [2 marks] Recall for a Lagrange Polynomial: (x-xo)(x - x₂) y = (x − x₁)(x - x₂) •Yo + (xox₁)(xox₂) (x-xo)(x-x₁) (x₂-xXo) (x₂-x₁) x₁) Y₂ (x₁ - x0)(x₁ - x₂) ₁ + (c) (i) Develop a Lagrange Polynomial to fit the data using the points for i = 1, 4 and 6. [4 marks] (ii) Use the Lagrange Polynomial to estimate the mass of water in air at 45°C. [2 marks] (iii) State the method which can be used to minimize problems with the Lagrange Polynomial. [1 mark] (d) Why are cubic spline approximations useful in chemical engineering? [2 marks]