Unit of coefficient of linear expansion
$
  {\text{A}}{\text{. }}{{\text{K}}^{ - 1}} \\
  {\text{B}}{\text{. }}{{\text{N}}^{ - 1}} \\
  {\text{C}}{\text{. }}{{\text{J}}^{ - 1}} \\
  {\text{D}}{\text{. }}{{\text{S}}^{ - 1}} \\
$

Hint: The coefficient of linear expansion is defined as the change in unit length of a material with unit change in temperature. Materials expand on raising the temperature so the coefficient of linear expansion is directly related to temperature.

Complete step-by-step answer:
Thermal Expansion: There occurs a change in dimensions of solid with change in temperature. As the temperature of the solid is increased, there is an increase in its volume or length. This phenomenon is called thermal expansion of the solid.

We can express the thermal expansion mathematically as the fractional change in length or volume of the solid with increase in temperature of that solid.

Linear expansion is the thermal expansion along the length of the solid. The change takes place only along one dimension. Volume expansion is defined as the thermal expansion along all three dimensions of the solid.

Coefficient of linear expansion is defined as a quantity which describes the amount of expansion taking place in a solid along a length with increase in temperature. It is the rate of change in unit length of the material with unit increase in temperature of the solid.

Formula for coefficient of linear expansion is given as :

${\alpha _L} = \dfrac{{dL}}{{dT}}$

where ${\alpha _L}$ is the coefficient of linear expansion,
$dL$ is the unit change in length of the solid
$dT$ is the unit change in temperature of the solid.

The S.I unit of thermal expansion is ${{\text{K}}^{ - 1}}$. Therefore the correct answer is option A.

Note: The coefficient of thermal expansion is an intrinsic property of a material. It depends on the intermolecular forces between the molecules of a material. Greater the attractive forces between the molecules, smaller is the change in length with temperature and smaller is the coefficient of linear expansion.