Question

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

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

Answer 1

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

Formula used: ${\gamma }_{app}={\gamma }_{real}-3\alpha$
Given: $\alpha =A,{\gamma }_{C{u}_{app}}=C,{\gamma }_{A{g}_{app}}=S,$
Let ${\gamma }_{real}=\gamma$
For copper
$C=\gamma -3A\dots \left(i\right)$
For silver
$S=\gamma -3a_{Ag}\dots \left(ii\right)$
From $\left(i\right)\text{and}\left(ii\right)$
$C+3A=S+3{\alpha }_{Ag}$
${\alpha }_{Ag}=\frac{C-S+3A}{3}$
Final answer: (b)