An equilateral triangle ABC is formed by two Cu rods AB and BC and one Al rod. It is heated in such a way that temperature of each rod increases by ∆T. Find change in the angle ABC. [Coeff. of linear expansion for Cu is α1 ,Coeff. of linear expansion for Al is α2 ]
Assuming that Triangle has taken any arbitrary shape,
Blue line is perpendicular to the base triangle of height h
Now since it forms two right angled triangles therefore, we can write
,
,
Simplifying further,
From 1 we can write
From triangle we can write
Substituting value of x
.
Re-arranging the terms we can write,
We have written an equation which is valid for triangles, therefore above equation will be valid for Equilateral (A=60)
Differentiating the above equation with its parameter,
Now we know that for equilateral angle
Change in lengths can be equated with thermal coeff,
,
,
Putting in equation,
Re-arranging the terms,
Couldn't generate an explanation.
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