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

Given the value of coefficient of volume expansion of $5\times {10}^{-4}{K}^{-1}$

As, original density of glycerine

$\begin{array}{c}\rho ={\rho }_0\left(1+Y\Delta T\right)\\ \Rightarrow \rho -{\rho }_0={\rho }_{0}Y\Delta T\end{array}$

Thus, fractional change in the density of glycerin for a rise of ${40}^{0}C$ in its temperature.

$\begin{array}{c}\frac{\rho -{\rho }_0}{{\rho }_0}=Y\Delta T=5\times {10}^{-4}\times 40\\ 200\times {10}^{-4}=0.020\end{array}$

.Hence,

option $C$ is correct answer.