The coefficient of volume expansion of glycerine is 49 x ${10}^{-5}{/}^0\mathrm{C}$. What is the fractional change in its density (approx.) for 30°C rise in temperature?

Coefficient of volume expansion of glycerine.
$\mathrm{\gamma }= 49\times {10}^{-5}/{ }^0\mathrm{C}$
Rise in temperature, $∆$T = 30°C

As $\mathrm{\gamma } = \frac{1}{∆\mathrm{T}}\left(\frac{∆\mathrm{V}}{\mathrm{V}}\right) \Rightarrow \frac{∆\mathrm{V}}{\mathrm{V}} = \mathrm{\gamma }\times ∆\mathrm{T}$

$\mathrm{or} \frac{∆\mathrm{V}}{\mathrm{V}} = (49\times {10}^{-5})\times 30 = 0.0147$

Since mass remains constant,
Fractional change in density = fractional change in volume = 0.0147 = 1.5 x ${10}^{-2}$