Question

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

• A. $0.0155$
• B. $0.0145$
• C. $0.0255$
• D. $0.0355$

Answer 1

Answer: (B)

Given, ${\alpha }_V=49\times 19^{-5}{}^{\circ }{C}^{-1}$
$\Delta T=30^{\circ }C$
$V^{\prime }=V+\Delta V=V\left(1+{\alpha }_V\Delta T\right)$
$\therefore V^{\prime }=V\left(1+49\times 10^{-5}\times 30\right)=1.0147V$
$\because \rho =\frac{m}{V}$ and ${\rho }^{\prime }=\frac{m}{V^{\prime }}=\frac{m}{1.0147V}=0.9855\rho$
Hence, fractional change in density
$=\frac{\rho -{\rho }^{\prime }}{\rho }=\frac{\rho -0.9855\rho }{\rho }=0.0145$