Question

A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of the vessel and liquid are ${\gamma }_v$ and ${\gamma }_L$respectively. If the system is heated, then the volume unoccupied by the percentage of liquid will necessarily :

• A. remain unchanged if ${\gamma }_V={\gamma }_L$
• B. increase if ${\gamma }_V={\gamma }_L$
• C. decrease if ${\gamma }_V={\gamma }_L$
• D. none of the above

Answer 1

The correct option is A remain unchanged if ${\gamma }_V={\gamma }_L$

$V_l=V_0(1+{\gamma }_l\Delta T)$
$V_g=V_0(1+{\gamma }_g\Delta T)$
If ${\gamma }_l={\gamma }_g$, $\Delta V_l=\Delta V_g$
where $\Delta V_l$ is the change in the volume of the liquid and $\Delta V_g$ is the change in the volume of the vessel.
$\therefore$ the volume unoccupied by the liquid will remain unchanged.