Question

The apparent coefficient of expansion of a liquid when heated in a copper vessel is $C$ and when heated in a silver vessel is $S$. If $A$ is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is -

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

Answer 1

The correct option is B $\frac{C+3A-S}{3}$

When a liquid expands in a vessel, we measure a value of the expanded liquid less than the actual value, owing to the expansion of the vessel.

Let -

${\gamma }_r$ = coefficient of real expansion of the liquid;

${\gamma }_a$ = coefficient of apparent expansion of the liquid;

${\gamma }_v$ = coefficient of expansion of the vessel.

We can write,

${\gamma }_r$ = ${\gamma }_a+{\gamma }_v$.

For copper,${\gamma }_r$ = $C$ + $3{\alpha }_{cu}$ = $C$ + $3A$;

for silver,${\gamma }_r$ = $S$ + $3{\alpha }_{Ag}$.

Comparing,

$C$ + $3A$ = $S$ + $3{\alpha }_{Ag}$

$\Rightarrow$ ${\alpha }_{Ag}$ = $\frac{C-S+3A}{3}$.