Derive αv = 3 αL for the coefficient of thermal expansion of materials. When X=Y=Z and change
temperature .
V = l03
∆V = Vf-Vo
= (lo+ ∆l)3 - l03
= (lo3+3lo2 ∆l+3lo ∆l2+∆lo3) - l03
= 3lo2 ∆l
from
∆ V = αvVo∆T
3lo2 ∆l = αvlo3∆T
αv = (3 ∆𝑙)/( lo∆T)
from
∆ l = α lo∆T
α = ∆ l / lo∆T
αv = 3 αL