Question

The value of coefficient of volume expansion of glycerin is $5 \times 10_ {-4} K_{-1}$. The fractional change in the density of glycerin for a rise of 40$^{\circ}$C in its temperature, is

• A. 0.025
• B. 0.010
• C. 0.015
• D. 0.020

Answer 1

Answer: (D)

Let $ p_0 \, \, and \, \, p_T $ be densities of glycerin at 0$^{\circ}$C and T$^{\circ}$C respectively. Then
$p_T = p_0 (1- \gamma \Delta) $
where $\gamma $is the coefficient of volume expansion of
glycerine and $\Delta T$ is rise in temperature.
$\frac{p _T}{ p_0} = 1- \gamma \Delta T \, \, or \, \, \gamma \Delta T = 1-\frac{p _T}{ p_0}$
Thus , $ \frac{p_0 - p_T}{p_0} = \gamma \Delta T $
Here, $ \gamma =5 \times 10_{-4} K_{-1} \, \, and \, \, \Delta T = 40^\circ C = 40 K$
$\therefore \, \, $ The fractional change in the density of glycerin
$ =\frac{p_0 - p_T}{p_0} = \gamma \Delta T = (5 \times 10 _{-4} K_{-1}) (40 K) =0.020$