Question

The coefficient of apparent volume expansion of a liquid in a copper vessel is $C$ and in a silver vessel is $S$. 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 $\frac{(C+{\gamma }_c-S)}{3}$

${\gamma }_{ac}={\gamma }_l-{\gamma }_c$
$\therefore C={\gamma }_l-{\gamma }_c$ .....(1)
${\gamma }_{as}={\gamma }_l-{\gamma }_s$
$\therefore S={\gamma }_l-{\gamma }_s$ ......(2)
From (1) and (2)
$S+{\gamma }_s=C+{\gamma }_c$
${\gamma }_s=C-S+{\gamma }_c$
$3{\alpha }_s=C-S+{\gamma }_c$
$\Rightarrow {\alpha }_s=\frac{C-S+{\gamma }_c}{3}$