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

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 $\gamma _{r}=C+3\alpha _{Cu}=C+3A$ .... $\left(\right.1\left.\right)$
For silver $\gamma _{r}=S+3\alpha _{Ag}$ .... $\left(\right.2\left.\right)$
from eq. $\left(\right.1\left.\right)$ and $\left(\right.2\left.\right)$
$\Rightarrow \, \, C+3A-S+3\alpha _{Ag}=0$
$\Rightarrow \, \alpha _{Ag}=\frac{C - S + 3 A}{3}$