Chapter 13, Problem 78A

To determine

Whether the coefficient of linear expansion depends on the unit of length used.

Explanation of Solution

Introduction: The coefficient of linear expansion is the rate of change of unit length per degree change in temperature.

Mathematically it is written as: ${\alpha }_L=\frac{dL}{dT}$

Where, ${\alpha }_L$ is the coefficient of linear expansion.

  $dL$ is the unit change in length.

  $dT$ is the unit change in temperature.

S.I unit of coefficient of linear expansion is $°C^{-1}or{K}^{-1}$

The coefficient of linear expansion is an intrinsic property of any material;thus,every material has different coefficient of linear expansion.

It is the cohesive force on which expansion of a material is totally dependent.

Hence, the coefficient of linear expansion depends on the material’s total length and not the unit of the length used.

Conclusion:Thus, the coefficient of linear expansion does not depend on the unit of the length used.