where , ll and l2 are initial and final lengths , Δt = change in temperature and α = coefficient of linear expansion .
Coefficient of linear expansion α = ( Δl / l * Δt )
where 1 = real length and Δl = change in length and Δt = change in temperature .
Superficial Expansion Expansion in area on heating is called superficial expansion . Increase in area A2 = A1 ( 1 + β Δt )
where , A1 and A2 are initial and final areas and β is a coefficient of superficial expansion .
Coefficient of superficial expansion β = ( ΔA / A * Δt ) where . A = area , AA = change in area and At = change in temperature .
Cubical Expansion Expansion in volume on heating is called cubical expansion . Increase in volume V2 = V1 ( 1 + γΔt )
where V 1 and V 2 are initial and final volumes and γ is a coefficient of cubical expansion .
Coefficient of cubical expansion
where V = real volume , AV = change in volume and Δt = change in temperature . Relation between coefficients of linear , superficial and cubical expansions β = 2α and γ = 3α Or α : β : γ = 1:2:3