24iff isotropic solids(i.e which have uniform expansion)
2 Answers
11right, eureka !!
@sunit
its simple........
L = Lo (1 + αθ)
A = Ao (1 + βθ)
or L2 = Lo2 (1 + βθ)
or [ Lo (1 + αθ) ]2 = Lo2 (1 + βθ)
or (1 + αθ)2 = (1 + βθ)
Using binomial ,
(1 + 2αθ) = (1 + βθ)
Hence , β = 2α
Similarly, for.
V = Vo (1 + γθ)
(1 + αθ)3 = (1 + γθ)
γ = 3α
Note : You may wonder, how A = L2 & V = L3 in all cases.This is only one particular case.In other cases you'll have A = L x B & V = L x B x H but you'll always get (1 + αθ)2 = (1 + βθ) & (1 + αθ)3 = (1 + γθ).
So, always (as in cases pointed out by "eureka") ......
β = 2α & γ = 3α .
