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.
$\frac{p_T}{p_0}=1-\gamma \Delta Tor\gamma \Delta T=1-\frac{p_T}{p_0}$
Thus , $\frac{p_0-p_T}{p_0}=\gamma \Delta T$
Here, $\gamma =5\times 10_{-4}{K}_{-1}and\Delta T=40^{\circ }C=40K$
$\therefore$ The fractional change in the density of glycerin
$=\frac{p_0-p_T}{p_0}=\gamma \Delta T=(5\times 10_{-4}{K}_{-1})(40K)=0.020$