Here, γ=49×10−5 K−1;
ΔT=30°C
Let there be m grams of glycerine and its initial volume be V. Suppose that the volume of the glycerine becomes V’ after a rise of temperature of 30°C then,
V′=V(1+γΔT)
=V(1+49×10−5×30)
or V′=1.0147 V
Initial density of the glycerine, ρ=

m

V

Final density of the glycerine,
ρ′=

m

V′

=

m

1.0147V

=

ρ

1.0147

=0.9855ρ
Therefore, fractional change in the value of density of glycerine,

ρ−ρ′

ρ

=

ρ−0.9855ρ

ρ

=0.0145