Question

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

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

Answer 1

The correct option is C $0.02$

We know that the density of a material is given by,
$\rho =\frac{M}{V}$, where, $M$ is mass and $V$ is volume.
So, $\frac{\Delta \rho }{\rho }=\frac{-\Delta V}{V}$ ........$\left(1\right)$
Also, volume expansion,
$\Delta V=\gamma V\Delta T$
$\Rightarrow \frac{\Delta V}{V}=\gamma \Delta T$
$\Rightarrow \frac{\Delta V}{V}=5\times {10}^{-4}\times 40$
$\Rightarrow \frac{\Delta V}{V}=0.020$
From $\left(1\right)$,
$\frac{\Delta \rho }{\rho }=-0.02$
Negative sign signifies that as temperature increases, volume increases and density decreases.