Question

Unit of coefficient of cubical expansion is
A. ${}^0{C^{ - 1}}$
B. ${K^{ - 1}}$
C. Both
D. None

Answer 1

Hint- Cubical expansion can also be said as the ratio of the difference in volume to that of the difference in the temperature. It is a material property.

Formula used: $\gamma = \dfrac{{{v_2} - {v_1}}}{{{v_1}\left( {{t_2} - {t_1}} \right)}}$
${v_1},{v_2}$ are the volume of the material
${t_1},{t_2}$ are the temperatures of the solid

Complete step by step answer:
The coefficient of cubical expansion is defined as the ratio of increase in the volume of a solid per degree in the rise of temperature to its initial volume.
Let us take the units of and substituting in the given equation we get,
$\gamma = \dfrac{{c{m^3}}}{{c{m^3}\left( K \right)}}$
$= \dfrac{1}{K}$
$= {K^{ - 1}}$
$\gamma$ has units ${}^0{C^{ - 1}}$ (CGS), ${K^{ - 1}}$(SI)
Hence option (C) Both is the correct answer

Additional information:
In general, all substances expand on heating. For example, when the metallic cap of a bottle is so tight, it is kept in hot water, this would allow the cap to expand and loosen it to unscrew easily. In the case of liquids, we can observe the expansion of mercury in a thermometer when it is put in hot water. In gases, it is observed that a cycle tube that is fully inflated may burst in hot summer due to the expansion of air in it.
Since solids have a definite shape, their expansion can be considered in terms of their length) linear expansion), area (areal expansion), and volume (cubical expansion). As different materials expand to different extents for the same rise in temperature, we need to define some quantity which will be a measure of the size or shape of any particular specimen of it and to differentiate between the various materials. The quantity is the coefficient of expansion of solids, which are of three types.
1. Coefficient of linear expansion: it is defined as the ratio of increase in the length of a solid per degree rise of temperature to its initial length.
2. Coefficient of areal expansion: it is defined as the ratio of increase in the area of a solid per degree rise of temperature to its initial area.
3. Coefficient of cubical expansion: it is defined as the ratio of increase in the volume of a solid per degree rise of temperature to its initial volume.

Note:
The magnitude of the coefficient of cubical expansion is very small thus it is not necessary to take the initial temperature as.
Solids expand on heating but their expansion is less compared to liquid and gases since in solids atoms or molecules are closely packed, few substances contract on heating that is, cast Iron, Bismuth, Indian rubber, etc.