Question

obtain the relation between coefficient of linear expansion & areal expansion​

Answer 1

Explanation:

The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. ...

The relationship between the area and linear thermal expansion coefficient is given as the following: αA=2αL α A = 2 α L .

Answer 2

Relationship:                   β = 2α

For coefficient of length expansion, we know that :-

• Δl ∝ l·
• Δl ∝ ΔT

So, we obtain :-

• Δl ∝ l· ΔT
• Δl = α l· ΔT
• α = Δl/ l· ΔT ______(1)

Similarly, for coefficient of areal expansion, we know that :-

• ΔA ∝ A·

• ΔA ∝ ΔT

So, we obtain :-

• ΔA ∝ A· ΔT
• ΔA = β A· ΔT
• β = ΔA/ A· ΔT ______(2)

We also know that :-

• A = l²

On partial differentiation, we obtain :-

• ΔA/A = 2 Δl/l

Dividing both sides by ΔT, we obtain :-

• ΔA/A ΔT = 2 Δl/l ΔT ____(3)

Hence, from (1), (2) and (3), we can conclude that :-

      β = 2α

i.e. coefficient of areal expansion is twice the coefficient of length expansion.