Question

A vessel of volume $1litre$ is filled with a liquid whose coefficient of volume expansion is $20$ times that of the vessel. At all temperatures if volume of air above the liquid is constant the volume of that empty space is:

• A. $950cc$
• B. $50cc$
• C. $1000cc$
• D. $500cc$

Answer 1

The correct option is A $950cc$

${\gamma }_l{V}_l={\gamma }_c{V}_c$

where
${\gamma }_l$- volume expansion coefficient of the liquid
${\gamma }_c$ - volume expansion coefficient of the container
$V_l$ - volume of the liquid
$V_c$ - volume of the container
Since the volume of the empty space above the liquid remains constant, $\Delta V_c=\Delta V_l$
$\therefore 20{\gamma }_c{V}_l={\gamma }_c{V}_c$
$\Rightarrow \frac{V_c}{V_l}=20$
$\frac{V_c-V_l}{V_c}=\frac{20-1}{20}=\frac{19}{20}$
$V_c-V_l=\frac{19}{20}\times 1litre=950ml=950cc$