Question

The coefficient of volume expansion of glycerin is $49\times {10}^{-5}{{}^{\circ }\text{C}}^{-1}$. The fractional change in the density on a $30{}^{\circ }\text{C}$ rise in temperature is

• A. $1.47\times {10}^{-2}$
• B. $1.47\times {10}^{-3}$
• C. $1.47\times {10}^{-1}$
• D. $1.47\times {10}^{-4}$

Answer 1

The correct option is A $1.47\times {10}^{-2}$

Given:
Coefficient of volume expansion of glycerin, $\gamma =49\times {10}^{-5}{{}^{\circ }\text{C}}^{-1}$
Change in temperature, $\Delta T={30}^{\circ }\text{C}$
We know that, due to thermal expansion, density as a function of temperature is given by,
$\rho =\frac{{\rho }_0}{(1+\gamma \Delta T)}$
$\Rightarrow \rho (1+\gamma \Delta T)={\rho }_0$
$\Rightarrow \rho -{\rho }_0=-\rho \gamma \Delta T$
$\Rightarrow \frac{\rho -{\rho }_0}{\rho }=-\gamma \Delta T$
$=-49\times {10}^{-5}\times 30=-1.47\times {10}^{-2}$

The negative sign indicates that the density decreases with increase in temperature.