A) \[(C+{{\gamma }_{C}}+S)/3\]
B) \[(C-{{\gamma }_{C}}+S)/3\]
C) \[(C+{{\gamma }_{C}}-S)/3\]
D) \[(C-{{\gamma }_{C}}-S)/3\]
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 |
| \[\Rightarrow \] \[{{\alpha }_{silver}}=\frac{{{\gamma }_{silver}}}{3}=\frac{C+{{\gamma }_{copper}}-S}{3}\] |
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