Question

The coefficient of volume expansion of glycerine is $49\times {10}^{–5}{/}^{\circ }C$. What is the fractional change in its density (approx.) for ${30}^{\circ }C$ rise in temperature?

• A. $2.8\times {10}^{–2}$
• B. $1.5\times {10}^{–2}$
• C. $2.5\times {10}^{–2}$
• D. $2.0\times {10}^{–2}$

Answer 1

The correct option is B $1.5\times {10}^{–2}$

We know that: $\frac{\Delta V}{V}=\gamma \times \Delta T$

Given: $\gamma =49\times {10}^{–5}/C°$, $\Delta T={30}^{\circ }C$
Coefficient of volume expansion of glycerine is given as
$\gamma =49\times {10}^{–5}/C^{\circ }$.
Rise in temperature, $\Delta T=30°C$
As we know
$\gamma =\frac{1}{\Delta T}\left(\frac{\Delta V}{V}\right)$
$\frac{\Delta V}{V}=\gamma \times \Delta T$
$\frac{\Delta V}{V}=(49\times {10}^{-5})\times 30$
$=0.0147$
Since mass remains constant,
Fractional change in density $=$ fractional change in volume $=0.0147=1.5\times {10}^{–2}$
Final answer (a)