The value of coefficient of volume expansion of glycerin is 5 ×10-4K-1  . The fractional change in the density of glycerin for a rise of 40°C in its temperature, is

Let ρ0 and ρT be densities of glycerin at 0°C and T°C respectively, then,ρT=ρ0(1-γΔT) where γ is the coefficient of volume expansion of glycerine  and ∆T is rise in temperature. ρTρ0=1-γΔT or γΔT=1-ρTρ0 Thus, ρ0-ρTρ0=γΔT Here, γ=5×10-4 K-1and ΔT=40°C=40 K∴ The fractional change in the density of glycerin =ρ0-ρTρ0=γΔT=5×10-4 K-1(40 K)=0.020