Question

A bimetal made of copper and iron strips welded together is straight at room temperature. It is held vertically so that the iron strip is towards the left hand and the copper strip is towards the right hand. The bimetal strip is then heated. The bimetal strip will:
( ${\alpha _{{\text{Cu}}}} = 16.6 \times 10 ^{- 6}\,{{\text{K}}^{ - 1}}$ and ${\alpha _{{\text{Fe}}}} = 12.0 \times 10 ^{- 6}\,{{\text{K}}^{ - 1}}$ )
(A) Remain straight
(B) Bend towards right
(C) Bend towards left
(D) Have no change

Answer 1

First we will examine the values of thermal expansion coefficient. A formula which gives the change in length is more helpful, which compares the change in length of the two metal strips.

Complete step by step answer:
In the given question, we are supplied with the following data:
A bimetal strip is taken into account. Both the metal strips are welded together.
Both the metal strips are straight at room temperature.
The metals are welded in such a way that the iron is present towards the left hand and the copper strip is present towards the right-hand side.
The bimetal strip is now heated.
Again, we are also provided the thermal expansion coefficient values:
For copper:
${\alpha _{{\text{Cu}}}} = 16.6 \times 10 ^{- 6}\,{{\text{K}}^{ - 1}}$
For iron:
${\alpha _{{\text{Fe}}}} = 12.0 \times 10 ^{- 6}\,{{\text{K}}^{ - 1}}$
We are asked to confirm whether there will be any change observed or not.
To begin with, we need to know that to transform a difference in temperature into mechanical displacement, a bimetallic strip is used.
Two layers, typically iron and copper, form the strip. Due to the difference in the expansion constants of the two materials, the two layers are fused together to form the strip. If heated, a flat strip will be bent in one direction (toward the iron part). The linear coefficient of thermal expansion compares the change in temperature to the change in the linear dimensions of a substance, and is the fractional change in the length of a bar per degree of change in temperature.
Again, we have a formula, which gives us the expansion of length when heated:
$\Delta L = \alpha {L_0}\Delta T$ …… (1)
Where,
$\Delta L$ indicates the change in length.
$\alpha$ indicates the thermal expansion coefficient value.
${L_0}$ indicates the original length.
$\Delta T$ indicates the change in temperature.
Since, we have:
${\alpha _{{\text{Cu}}}} > {\alpha _{{\text{Fe}}}}$
So, from equation (1), we can obviously write that:
$\Delta {L_{{\text{Cu}}}} > \Delta {L_{{\text{Fe}}}}$
That is, we can say that copper expands more than that of iron.

Hence, the strip will bend towards the iron strip i.e. bend towards left.Thus,the correct option is C.

Note: While answering this question many students seem to have a confusion regarding the direction of bending. If the metal with greater expansion coefficient value is present on left, then it will bend towards right, as it cannot bend towards right itself. If it bends towards right itself, then it would mean that the other metal bends too along with this metal which is false.