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