Let r0 and rT be densities of glycerin at 0∘C and T∘C respectively. Then, ρT=ρ0(1−γ∆T) where γ is the coefficient of volume expansion of glycerine and ∆T is rise in temperature.
ρT
ρ0
=1−γ∆T⇒γ∆T=1−
ρT
ρ0
Thus,
ρ0−ρT
ρ0
=γ∆T Here, γ=5×10−4K−1 and ∆T=40∘C=40K ∴ The fractional change in the density of glycerin =