Question

If $\gamma$ of a solid container is x% of $\gamma$ (real) of a liquid, the volume fraction of the container which should be filled with that liquid to keep that unoccupied volume above the liquid in it constant at all temperatures is

• A. x${}^2$%
• B. (x-1)%
• C. (x+1)%
• D. x%

Answer 1

Answer: (D)

x%

When the volume expansion of the liquid is same as that of the container,
${\gamma }_{container}{v}_{container}={\gamma }_{liquid}{v}_{liquid}$
$\Rightarrow x{\gamma }_{liquid}{v}_{container}={\gamma }_{liquid}{v}_{liquid}$
$\Rightarrow \frac{v_{liquid}}{v_{container}}=x$
Hence, $x\%$ of the container should be filled with the liquid to keep the unoccupied volume above the liquid constant.