Question

State the relationship between the three expansion coefficients of a solid.

Answer 1

1. When a metal rod is heated its length increases this is called linear expansion.
2. The coefficient of linear expansion$\left(\mathrm{\alpha }\right)$ of the material of a solid rod or wire is defined as the increase in its length per unit of original length per degree rise in temperature.
3. When a metallic sheet is heated, its surface area increases this is called the superficial or area expansion.
4. The coefficient of superficial expansion$\left(\mathrm{\beta }\right)$ of the material of a solid thin sheet is defined as the increase in its surface area per unit of original surface area per degree rise in temperature.
5. When a solid metallic bulk solid like a cube, or a cuboid is heated, its volume increases this is called volume expansion of solid.
6. The coefficient of volume expansion$\left(\mathrm{\gamma }\right)$ of the material of bulk solid is defined as the increase in its volume per unit of original volume per degree rise in temperature.
7. It is observed that for a given material the value of the coefficient of area expansion is twice the coefficient of linear expansion of that material.
8. That is $\mathrm{\beta }=2\mathrm{\alpha }$
9. It is also observed that for a given material the value of the coefficient of volume expansion is thrice the coefficient of linear expansion of the same material.
10. This is $\mathrm{\gamma }=3\mathrm{\alpha }$
11. From these two relations, it can be concluded that the relationship between the coefficients of thermal expansion of solid is:
12. $\mathrm{\alpha }:\mathrm{\beta }:\mathrm{\gamma }=1:2:3$