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. $(C+{\gamma }_C+S)/3$
• B. $(C-{\gamma }_C+S)/3$
• C. $(C+{\gamma }_C-S)/3$
• D. $(C-{\gamma }_C-S)/3$

Answer 1

The correct option is C $(C+{\gamma }_C-S)/3$

Apparent coefficient of volume expansion for liquid ${\gamma }_{app}={\gamma }_L-{\gamma }_s$ $\therefore$ ${\gamma }_L={\gamma }_{app}+{\gamma }_s$
where $\gamma$${}_s$ is coefficient of volume expansion for solid vessel.
When liquid is placed in copper vessel then $\gamma$${}_L$ = C + $\gamma$${}_{copper}\dots \dots \left(i\right)$ [As $\gamma$${}_{app.}$ for liquid in copper vessel = C]
When liquid is placed in silver vessel then $\gamma$${}_L$ = S + $\gamma$${}_{silver}\dots \dots \left(ii\right)$[As $\gamma$${}_{app.}$ for liquid in silver vessel = S]
From equation (i) and (ii) we get C + $\gamma$${}_{copper}$ = S + $\gamma$${}_{silver}$
$\therefore$ ${\gamma }_{silver}=C+{\gamma }_{copper}-S$
Coefficient of volume expansion = 3 $\times$ Coefficient of linear expansion
$\Rightarrow$ ${\alpha }_{silver}=\frac{{\gamma }_{silver}}{3}=\frac{C+{\gamma }_{copper}-S}{3}$