RELATION BETWEEN THE THREE COEFFICIENTS OF THERMAL EXPANSION

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Solution

$C o e f f i c i e n t o f l i n e a r e x p a n s i o n = α C o e f f i c i e n t o f s u p e r f i c i a l e x p a n s i o n = β a n d C o e f f i c i e n t o f c u b i c a l e x p a n s i o n = γ B u t L = L_{0} (1 + α ∆ T) a n d A = A_{0} (1 + β ∆ T) = L^{2} {(1 + α ∆ T)}^{2} = L^{2} (1 + 2 α ∆ T) O n c o m p a r i s i o n w e g e t, β = 2 α . S i m i l a r l y V = V_{0} (1 + γ ∆ Y) = L^{3} (1 + 3 α ∆ T) S o γ = 3 α . O n c o m p a r i s i o n w e g e t, α = β / 2 = γ / 3 . T h i s i s t h e r e q u i r e d r e l a t i o n .$

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