# Derive a relation between coefficient of linear expansion and coefficient of cubical expansion

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by Utsavsterbon

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by Utsavsterbon

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The Brainliest Answer!

change in length=Δl

original volume=v

change in volume=Δv

initial volume=l³

final volume(v+Δv)=(l+Δl)³

change in volume=final volume-initial voluma

Δv=l³+Δl³+3lΔl(l+Δl)-l³

Δv=l³+Δl³+3lΔl²+3l²Δl-l³

Δl³is neglected bcoz it is too small

Δv=3l²Δl+3lΔl²

we will also ignore 3lΔl²

Δv=3l²Δl

we know that

coefficient of volumetric expansion

y=Δv/v×Δt

y=3l²Δl/l³×Δt

y=3Δl/l×Δt {Δl/l×Δt=α}

y=3α