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. 0.01
• B. 0.015
• C. 0.02
• D. 0.025

Answer 1

The correct option is C 0.02

The value of coefficient of volume expansion of glycerin , $\gamma$ = $5\times {10}^{-4}{K}^{-1}$.
New density of glycerine is
$\begin{array}{c}\rho ={\rho }_0\left(1+\gamma \Delta T\right)\\ \Rightarrow \rho -{\rho }_0={\rho }_0\gamma \Delta T\end{array}$
Thus, fractional change in the density of glycerin for a rise of ${40}^{\circ }C$ in its temperature is
$\begin{array}{c}\frac{\rho -{\rho }_0}{{\rho }_0}=\gamma \Delta T=5\times {10}^{-4}\times 40\\ =200\times {10}^{-4}=0.020\end{array}$.