Question

give a relation between coefficient of areal expansion and coefficient of volume expansion ​

Answer 1

Answer:

We have to find a relationship between areal expansion coefficient (β) and volume expansion coefficient (γ).

This is possible only by comparing both the terms with linear expansion coefficient.

We need to remember the following relations:

$\bigstar \: volume \: exp = 3(linear \: exp ) \\ = > \gamma = 3 \alpha$

Again, we can say that :

$\bigstar \: areal \: exp = 2(linear \: exp ) \\ = > \beta = 2 \alpha$

Dividing the above 2 Equations :

$= > \dfrac{ \gamma }{ \beta } = \dfrac{3 \cancel \alpha }{ 2\cancel \alpha }$

$= > \beta = \dfrac{2}{3} \gamma$

So final answer :

$\boxed{ \red{ \huge{ \bold{\beta = \dfrac{2}{3} \gamma }}}}$

Additional information on expansion coefficients :

• Expansion coefficients are material dependent.
• They don't depend on the size of the objects
• They are of the order 10^(-6) units

Answer 2

$\tt{\green{Solution \: :- }}$

We know that :

Linear expansion refers to expansion in 1-D and is referred by Alpha. Dimension : L

Areal expansion refers to expansion in 1-D and is referred by Beta. Dimension : L^2

Volume expansion refers to expansion in 1-D and is referred by Gamma . Dimension : L^3

Hence:

$\beta = \dfrac{2}{3} \gamma$