Triple metals
Two metal sticks
A
and
B
are fixed on the left wall in the above diagram. The lengths and the linear expansion coefficients of
A
and
B
are
,
and
,
, respectively. A third metal stick
C
with length
is fixed on the right joint bar on which the right end of
B
is also fixed. Suppose that there is a temperature change
which is the same for all of
A
,
B
and
C
, and the distance between the wall and
C
remains constant, which is
as shown in the diagram. What is the linear expansion coefficients of the metal
C
?
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1 solution
In the given question :
Let coefficient of linear expansion of rod c be x;
{ Here change in temperature is represented by T }
For rod A ( Final Length ) : 3L(1+ aT)
For rod B ( Final Length ) : L(1+ 2aT)
For rod C ( Final Length ) : 3L(1+xT)
It is given that for all temperatures :
L(A) + L(B) - L(C) = Lo
3L + 3LaT + L + 2LaT - 3L - 3LxT = Lo
On differentiating the given equation :
3La + 2La - 3Lx = 0
5a=3x
x= 5a/3