A solid whose volume does not change with temperature  floats in a liquid. For two different temperatures t1 and t2 of the liquid, fractions f1 and f2 of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

As with the rise in temperature, the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.Fraction of solid submerged at t1∘C=f1=Volume of displaced liquid =V01+γt1 …….. (i)and fraction of solid submerged at t2∘C=f2= Volume of displaced liquid =V01+γt2 ………. (ii)From Eqs. (i) and (ii), f1f2=1+γt11+γt2⇒γ=f1−f2f2t1−f1t2