Question

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

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

Answer 1

The correct option is C $0.020$

Given:
Coefficient of volume expansion of glycerin, $\gamma =5\times {10}^{-4}{{}^{\circ }\text{C}}^{-1}$
Change in temperature, $\Delta T={40}^{\circ }\text{C}$
We know that, due to thermal expansion, density as a function of temperature is given by, $\rho =\frac{{\rho }_0}{(1+\gamma \Delta T)}$
$\Rightarrow \rho (1+\gamma \Delta T)={\rho }_0$
$\Rightarrow \rho -{\rho }_0=-\rho \gamma \Delta T$
$\Rightarrow \frac{\rho -{\rho }_0}{\rho }=-\gamma \Delta T$
$=-5\times {10}^{-4}\times 40=-0.020$
The negative sign indicates that the density decreases with increase in temperature.