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 ${40}^{o}C$ in its temperature, is:

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

Answer 1

The correct option is B 0.02

$V=V_0(1+\gamma \Delta T)$
$V=V_0+V_0\gamma \Delta T$
$\frac{V-V_0}{V_0}=\gamma \Delta T$
Now since mass $M$ is constant
$\frac{\frac{M}{\rho }-\frac{M}{{\rho }_0}}{\frac{M}{{\rho }_0}}=\gamma \Delta T$
$\frac{{\rho }_0-\rho }{\rho }=\gamma \Delta T$
multiplying and divdiing by ${\rho }_0$
$\frac{{\rho }_0-\rho }{\rho }\frac{{\rho }_0}{{\rho }_0}=\gamma \Delta T$
$\frac{{\rho }_0}{\rho }=\frac{V}{V_0}=1+\gamma \Delta T$
$\frac{{\rho }_0-\rho }{{\rho }_0}=\frac{\gamma \Delta T}{1+\gamma \Delta T}$