Question

Indicate the relation between co-efficient of
linear expansion (x) and co-efficient of areal
expansion (B)​

Answer 1

Answer:

Coefficient of Linear Expansion (α)

The ratio of increase in length of a solid per degree rise in temperature to its original length is called Co-efficient of linear expansion (α)

$\implies \rm \alpha = \dfrac{l_2 - l_1}{l_1 \times (t_2 - t_1)} /^0C$

Co-efficient of areal  expansion (β)

The ratio of increase in its area per degree rise in temperature to it's original area is called Co-efficient of areal  expansion (β)

$\rm \implies \beta = \dfrac{A_2 - A_1}{A_1 \times (t_2 - t_1)} /^0C$

Let us take,

⇒ Co-efficient of linear expansion is α

⇒ Co-efficient of areal  expansion is β

The relationship between α and β is given as

$\boxed{\boxed{\sf \alpha = \dfrac{\beta }{2} }}$

Additional information:

Coefficient of volume expansion (γ)

The ratio of increase in its volume per degree rise in temperature to it's original volume is called Co-efficient of volume expansion (γ)

$\rm \implies \gamma = \dfrac{V_2 - V_1}{V_1 \times (t_2 - t_1)} /^0C$

Relation among α, β, γ

⇒ β = 2α

⇒ γ = 3α

Therefore,

α : β : γ = 1 : 2 : 3

Hence,

$\purple{\boxed{\boxed{\alpha = \dfrac{\beta }{2} = \dfrac{\gamma}{3} }}}$