Answer to Question #281585 in MatLAB for Jack lakos

Question

1. The change in the heat capacity of a substance due to temperature is given in the table below. Calculate the heat required to raise the temperature of 1-mole of the substance from 300 K to 1000 K using (a) Trapezoidal rule and (b) Simpson’s rule.

(Hint: )

T (K) / C_p (Cal/mol.K)

300 19.65

400 26.74

500 32.80

600 37.74

700 41.75

800 45.6

900 47.83

1000 50.16

1. Integrate the function below between the limits 0 and 0.8 by (a) Trapezoidal rule and (b) Simpson’s rule.

Answer 1

T = [300, 400, 500, 600, 700, 800, 900, 1000]; % K
Cp = [19.65, 26.74, 32.80, 37.74, 41.75, 45.6, 47.83, 50.16]; % Cal/mol.K

dT = 100;   % interval width K
Q_trap = (Cp(1)/2 + sum(Cp(2:7)) + Cp(8)/2) * dT

Q_simp = (Cp(1) + 4*sum(Cp(2:2:7)) + 2*sum(Cp(3:2:6)) + Cp(7)) * dT/3;
% As the number of intervals is odd, the last interval calculated 
% using trapezoidal rule
Q_simp = Q_simp + (Cp(7)+Cp(8)) * dT/2