Question 50: Thermodynamics & KTG

Question

The coefficient of volume expansion of glycerine is $$49 	imes 10^{-5} \mathrm{~K}^{-1}$$. The percentage change in its density for a $$50^{\circ} \mathrm{C}$$ rise in temperature is

Accepted Answer

The coefficient of volume expansion ($$\beta$$) is given as $$49 	imes 10^{-5} \mathrm{~K}^{-1}$$. The formula to determine the change in volume due to thermal expansion is:
$$ \Delta V = V \beta \Delta T $$
Here:
$$\Delta V$$ is the change in volume.
$$V$$ is the original volume.
$$\beta$$ is the coefficient of volume expansion.
$$\Delta T$$ is the change in temperature.
Given that the temperature change ($$\Delta T$$) is $$50^{\circ} \mathrm{C}$$, we have:
$$ \Delta V = V \cdot (49 	imes 10^{-5} \mathrm{~K}^{-1}) \cdot 50 $$
$$ \Delta V = V \cdot (49 	imes 10^{-5} 	imes 50) $$
$$ \Delta V = V \cdot (2450 	imes 10^{-5}) $$
$$ \Delta V = V \cdot 0.0245 $$
This indicates that the volume increases by 2.45%. Since density ($$ho$$) is inversely proportional to volume ($$V$$), a 2.45% increase in volume will result in a 2.45% decrease in density.
Thus, the percentage change in density is 2.45%. Hence, the correct option is:
Option D: 2.45

Answer

3.54

Answer

5.24

Answer

4.25

Answer

2.45

Thermodynamics & KTG

The coefficient of volume expansion of glycerine is $49 \times 10^{-5} \mathrm{~K}^{-1}. The percentage change in its density for a 50^{\circ} \mathrm{C}$ rise in temperature is

Choose the correct answer: