Question

Coefficient of linear expansion generally …………. With the increase in temperature.
A. increases
B. decreases
C. remains the same
D. doubles itself

Answer 1

Hint: Concept of thermal expansion and linear expansion effect of temperature or heat causes linear expansion but term coefficient of linear expansion is a constant that depends on type of material.

Complete step by step solution:
Thermal expansion: Almost all the solids, gases and liquids expand on heating. This increase in size of a body when it is heated is called thermal expansion.
It is of three types
(i) Linear expansion
(ii) Superficial expansion
(iii) Cubical expansion
We will discuss the coefficient of linear expansion.
Coefficient of linear expansion: Suppose a solid rod of length L is heated by $\mathrm{\Delta }T$such that its final length becomes$L^{\prime }$. From experiments, it is clear that
(i) Increase in length $\times$ rise in temperature
So, $L^{\prime }-L\propto \mathrm{\Delta }T...(i)$
(ii) Increase in length $L^{\prime }-L\propto L...(ii)$
Combining (i) and (ii)
$$\begin{gathered} L^{\prime }-L\propto L\mathrm{\Delta }T \\ {L}^{\prime }-L=\alpha L\mathrm{\Delta }T \end{gathered}$$
Where $\alpha$ is a proportionality constant and is called coefficient of linear expansion.
$$\begin{gathered} \Rightarrow L^{\prime }=L+\alpha L\mathrm{\Delta }T \\ \Rightarrow L^{\prime }=L\left[1+\alpha \mathrm{\Delta }T\right] \\ \Rightarrow \alpha ={\displaystyle \frac{L^{\prime }-L}{L\mathrm{\Delta }T}} \\ \Rightarrow \alpha ={\displaystyle \frac{\mathrm{\Delta }L}{L\mathrm{\Delta }T}} \end{gathered}$$

Coefficients of linear expansion measure the fractional change in size per degree change in temperature at constant pressure.
From above, it is clear that $\alpha$ is coefficient of linear expansion and is constant. So, it is independent of temperature.

Hence, the coefficient of linear expansion remains the same with the increase in temperature.

Hence, the correct option is (C).

Note: Coefficient of linear expansion just determines the change in length with respect to temperature and initial length but itself is independent of temperature.