Thermal Properties of Matter - Result Question 3
3. 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:
[2015 RS]
(a) 0.020
(b) 0.025
(c) 0.010
(d) 0.015
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Answer:
Correct Answer: 3. (a)
Solution:
- (a) From question,
Rise in temperature $\Delta t=40^{\circ} C$
Coefficient of volume expansion
$\gamma=5 \times 10^{-4} K^{-1}$
Fractional change in the density $\frac{\Delta \rho}{\rho_0}=\frac{\rho_0-\rho_T}{\rho_0}$
$\rho_T=\rho_0(1-\gamma \Delta t)$
$\Rightarrow \frac{\Delta \rho}{\rho_0}=\frac{\rho_0-\rho_T}{\rho_0}=\gamma \Delta T=(5 \times 10^{-4})(40)=0.020$
Most substances (solid & liquid) expand when they are heated, so volume of a given mass of a substance increases on heating so density decreases as
$ \begin{aligned} & \rho \propto \frac{1}{V} \Rightarrow \frac{\rho^{\prime}}{\rho}=\frac{V}{V^{\prime}}=\frac{V}{V+\Delta V} \\ & =\frac{V}{V+\gamma V A \theta}=\frac{1}{1+\gamma \Delta \theta} \end{aligned} $
