Properties Of Solids And Liquids Question 562
Question: The coefficient of apparent expansion of a liquid in a copper vessel is C and in a silver vessel S. The coefficient of volume expansion of copper is $ {\gamma _{C}} $ . What is the coefficient of linear expansion of silver?
Options:
A) $ (C+{\gamma _{C}}+S)/3 $
B) $ (C-{\gamma _{C}}+S)/3 $
C) $ (C+{\gamma _{C}}-S)/3 $
D) $ (C-{\gamma _{C}}-S)/3 $
Show Answer
Answer:
Correct Answer: C
Solution:
Apparent coefficient of volume expansion for liquid $ {\gamma _{app}}={\gamma _{L}}-{\gamma _{s}} $
$ \therefore $ $ {\gamma _{L}}={\gamma _{app}}+{\gamma _{s}} $
where $ {\gamma _{s}} $ is coefficient of volume expansion for solid vessel.
When liquid is placed in copper vessel, then
$ {\gamma _{L}}=C+{\gamma _{copper}} $ (i)
[as $ {\gamma _{app}} $ for liquid in copper vessel = C]
When liquid is placed in silver vessel, then
$ {\gamma _{L}}=S+{\gamma _{silver}} $
[as $ {\gamma _{app}} $ for liquid in silver vessel = S]
From (i) and (ii), we get
$ C+{\gamma _{copper}}=S+{\gamma _{silver}} $
$ \therefore $ $ {\gamma _{silver}}=C+{\gamma _{copper}}-S $
Coefficient of volume expansion $ =3\times $ Coefficient of linear expansion
$ \Rightarrow $ $ {\alpha _{silver}}=\frac{{\gamma _{silver}}}{3}=\frac{C+{\gamma _{copper}}-S}{3} $
