Question

The coefficient of apparent expansion of a liquid in a copper vessel is $C$ and in a silver vessel $S$. The coefficient of volume expansion of copper is ${\gamma }_C$. What is the coefficient of linear expansion of silver

• A. $\frac{C+{\gamma }_C+S}{3}$
• B. $\frac{C-{\gamma }_C+S}{3}$
• C. $\frac{C+{\gamma }_C-S}{3}$
• D. $\frac{C-{\gamma }_C-S}{3}$

Answer 1

The correct option is C

$\frac{C+{\gamma }_C-S}{3}$

Apparent coefficient of volume expansion for liquid

${\gamma }_{app}$ = ${\gamma }_L$ - ${\gamma }_s$

$\therefore$ ${\gamma }_L$ = ${\gamma }_{app}$ + ${\gamma }_s$

Where ${\gamma }_s$ is coefficient of volume expansion for solid vessel.

When liquid is placed in copper vessel

${\gamma }_L$ = $C$ + ${\gamma }_{copper}$ .................(i)

(As ${\gamma }_{app}$ for liquid in copper vessel = $C$)

When liquid is placed in silver vessel

${\gamma }_L$ = $S$ + ${\gamma }_{silver}$ ................(ii)

(As ${\gamma }_{app}$ for liquid in silver vessel = $S$)

From Eqs.(i) and (ii), we get $C$ + ${\gamma }_{copper}$ = $S$ + ${\gamma }_{silver}$

$\therefore$ ${\gamma }_{silver}$ = $C$ + ${\gamma }_{copper}$ - $S$

Coefficient of volume expansion = 3 $\times$ Coefficient of linear expansion

$\Rightarrow$ ${\alpha }_{silver}$ = $\frac{{\gamma }_{silver}}{3}$ = $\frac{C+{\gamma }_{copper}-S}{3}$