Three
equal-length straight rods, of aluminium, invar, and steel, all at ,
form an equilateral triangle with hinge pins at the vertices. We have
to find the temperature at which the angle opposite the invar rod
will become .
The linear thermal
coefficients of these materials are
The
linear thermal coefficients of these materials are
,
,
and .
Let l
be the length of the rods at .
When the temperature of the rods becomes
the changes in the lengths of the rods will be determined by the
coefficients of their linear expansion. We have
,
,
and
Using the trigonometric
property of a triangle that
,
we have the relation,
Neglecting
terms of order
,
we get
Substituting
the values of
,
,
and
,
we solve the above equation for
.
We find
.
Therefore,
the temperature at which the angle opposite the invar bar will
become
will be
.
,
form an equilateral triangle with hinge pins at the vertices. We have
to find the temperature at which the angle opposite the invar rod
will become
.
,
and
.
he
linear thermal coefficients of these materials are
the changes in the lengths of the rods will be determined by the
coefficients of their linear expansion. We have
,
,
,
,
we get
,
,
and
,
we solve the above equation for
.
We find
.
will be
.