Question

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

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

Answer 1

The correct option is D 0.02


$V=V_0[1+\gamma \Delta T]\therefore d=\frac{M}{V}\frac{M}{d_T}=\frac{M}{d_0}[1+\gamma \Delta T]d_T=\frac{d_0}{1+\gamma \Delta T}{d}_T=d_0(1-\gamma \Delta T)d_T=d_0-d_0\gamma \Delta T{d}_0\gamma \Delta T=d_0-d_T\left[\frac{d_0-d_T}{d_0}\right]=\gamma \Delta T$
Fraction change in density =$\gamma \Delta T$
$=5\times {10}^{-4}\times 40K=0.020$