Question

The S.I unit for the coefficient of linear expansion is
A) $^\circ {\text{C}}$
B) Per $^\circ {\text{C}}$
C) ${\text{c}}{{\text{m}}^2}/^\circ {\text{C}}$
D) None of these

Answer 1

When the length of a body changes with an increase in the temperature, the phenomenon is referred to as linear expansion. The coefficient of linear expansion can be defined as the change in the length of the body which is one unit long due to a rise of $1^\circ {\text{C}}$ in the temperature.

Formula used:
-The coefficient of linear expansion of a material is given by. ${\alpha _l} = \dfrac{{\Delta l}}{{l\Delta T}}$ where $\Delta l$ is the change in length of the material, $l$ is the original length and $\Delta T$ is the change in temperature.

Complete step by step solution:
Step 1: Express the relation for the change in length due to temperature to obtain an expression for the coefficient of linear expansion.
The change in length of a material due to a change in temperature is given by, $\Delta l = {\alpha _l}l\Delta T$ where ${\alpha _l}$ is the coefficient of linear expansion, $\Delta l$ is the change in length of the material, $l$ is the original length and $\Delta T$ is the change in temperature.
From the above relation, we obtain the expression for the coefficient of linear expansion as ${\alpha _l} = \dfrac{{\Delta l}}{{l\Delta T}}$ ------- (1)
Step 2: Express equation (1) in terms of the S.I units of the physical quantities involved.
The S.I unit of length $l$ and change in length $\Delta l$ is metre.
The S.I unit of temperature is degree Celsius or Kelvin.
So expressing the right-hand side of equation (1) in terms of the respective S.I units of length, change in length and change in temperature we have ${\alpha _l} = \dfrac{{{\text{metre}}}}{{{\text{metre}} \times {\text{degree Celsius}}}} = \dfrac{1}{{{\text{degree Celsius}}}}$
Thus the S.I unit of the coefficient of linear expansion will be per $^\circ {\text{C}}$ .

So the correct option is B.

Note: The change in length of the body can be a decrease or an increase in the length. However, expansion suggests that the length of the material increases. The coefficient of linear expansion is an intrinsic property of the material of the body and so it will be different for different materials. It is essentially the rate at which a body expands.