A solid whose volume does not change with temperature floats in a liquid. For two different temperatures `t_1` and `t_2` of the liqiud, fraction `f_1` and `f_2` of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

Explanation

If `V_(0)` is the initial valume of the liquid
`DeltaV_(1)` is the volume of the liquid displaced at `t_(1)^(0)C`
`DeltaV_(2)` is the volume of the liquid displaced at `t_(2) ^(0)C`
`f_(1) = (DeltaV_(1))/(V_(0)), f_(2) = (DeltaV_(1))/(V_(0)), (f_(1))/(f_(2)) = (DeltaV_(1))/ (DeltaV_(2))`
`(f_(1))/(f_(2)) = (V_(0)(1 + gammat_(1)))/(V_(0)(1 + gammat_(2))), f_(1) + f_(1)gammat_(2) = f_(2) + f_(2)gammat_(1)`
`gamma = (f_(1) - f_(2))/(f_(2)t_(1) - f_(1)t_(2))`