Question

The fraction of the volume of a glass flask that must be filled with mercury so that the volume of the empty space may be the same at all temperatures is given by $({\alpha }_{glass}=9\times {10}^{-6/0}C,{\gamma }_{Hg}=18.9\times {10}^{-5/0}C)$

• A. $\frac{1}{2}$
• B. $\frac{1}{7}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{1}{7}$

When change in volume of mercury after expansion is equal to change in volume of the glass tube after expansion, the empty space will be same at all temperatures.
$\Delta V_l=\Delta V_g$
Volume will be directly proportional to height.
$h_l$ and $h_g$ are heights of liquid and glass respectively after expansion.
$\Rightarrow h_l{\gamma }_l=h_g{\gamma }_g$

$\Rightarrow \frac{h_g}{h_l}=\frac{{\gamma }_l}{{\gamma }_g}=\frac{18.9\ast {10}^{-5}}{3\ast 9\ast {10}^{-6}}$ since ${\gamma }_g=3{\alpha }_g$

$\Rightarrow \frac{h_g}{h_l}=7$

$\Rightarrow \frac{h_l}{h_g}=\frac{1}{7}$