A long cylindrical metal vessel, having a linear coefficient `(alpha)`, is filled with a liquuid upto a certain level. On heating it, it is found that the level of liquid in the cylinder reamains the same. What is the cylinder reamains the same. What is the volume coefficient of expansion of the liquid?

Explanation

Volume of liquid `V = Al.` increase is volume
`DeltaV = (DeltaA)l` (`:.l` is constant)

For container: `(DeltaV)_(C) = (DeltaA)l = AbetaDeltatl = V(2alpha)Deltat`
For liquid: `(DeltaV)_(t) = Vgamma_(1)Deltat`
If the level of the liquid remains same
`(DeltaV)_(C) = (DeltaV)_(t), V(2alpha)Deltat = Vgamma_(1)Deltat`
`rArr gamma_(1) = 2alpha`