Question

The remaining volume of a glass vessel is constant at all temperatures if $\frac{1}{x}$ of its volume is filled with mercury. The coefficient of volume is filled with mercury. The coefficient of volume expansion of mercury is 7 times that of glass. The value of $x$ should be

• A. 5
• B. 7
• C. 6
• D. 8

Answer 1

The correct option is B

7

Let temperature is increased by $\Delta T$.

$V_g-V_{Hg}$ = $V-\frac{V}{x}$ at all temperature

$V[1+{\gamma }_g\Delta T]-\frac{V}{x}[1+{\gamma }_{Hg}\Delta T]$ = $V-\frac{V}{x}$

$\Rightarrow$ ${\gamma }_g$ = $\frac{{\gamma }_{Hg}}{x}$ $\Rightarrow$ ${\gamma }_g$ = $\frac{7{\gamma }_g}{x}$ $\Rightarrow$ $x$ = $7$