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

Answer: (B)

${\gamma }_r={\gamma }_a+{\gamma }_v$
where ${\gamma }_r$ = coefficient of real expansion,
${\gamma }_a$ = coefficient of apparent expansion and
${\gamma }_v$ = coefficient of expansion of vessel.
For copper ${\gamma }_r=C+3{\alpha }_{Cu}=C+3A$ .... $(1)$
For silver ${\gamma }_r=S+3{\alpha }_{Ag}$ .... $(2)$
from eq. $(1)$ and $(2)$
$\Rightarrow C+3A-S+3{\alpha }_{Ag}=0$
$\Rightarrow {\alpha }_{Ag}=\frac{C-S+3A}{3}$