Answer:
a) D = 4.88 * 10^(-14) m^2 / s
b) <em>t </em>= 1.1 hr
Solution:
a) Magnesium in Aluminum diffusion:
D = Do * exp(-Qd / RT)
= (1.2 * 10^(-4) m^2 / s) * exp ( - 130,000 / 8.31 * 723.15)
= 4.88 * 10^(-14) m^2 / s
D = 4.88 * 10^(-14) m^2 / s
b) The composition remains same at say the distance Xo:
(Cx - Co) / (Cs - Co) = Constant
Xo^2 / D_{550} * <em>t </em>= Xo^2 / D_{450} * 15
D_{550} * <em>t </em>= D_{450} * 15
(1.2 * 10^(-4) m^2 / s) * exp ( - 130,000 / 8.31 * 723.15) * <em>t</em>
(4.88 * 10^(-14) m^2 / s) * 15
by, solving for <em>t </em>we get:
<em>t </em>= 1.1 hr
So, the time required is 1.1 hr.
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Answer:
System of linear equations is solved below and explained in detail.
Explanation:
Part a:
M = [1 3 5 2; 2 -4 7 -3; 0 -4 -7 3; 5 -3 2 1];
c = [7; -3; -1; 0];
Part b:
The statement used for the solution of system of linear equation will be:
X = linsolve(M,c)
where X will give the values of x1, x2, x3, x4 respectively.
Part c:
The system is solved in matlab using above equation and the results are attached in a file.
The values for X are:
x1 = -2/7
x2 = 3/7
x3 = 4/7
x4 = 11/7
