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
A. `(C+gamma_C+S)//3`
B. `(C-gamma_C+S)//3`
C. `(C+gamma_C+S)//3`
D. `(C-gamma_C-S)//3`

Answer 1

Correct Answer - C
Apparent coefficient of volume expansion for liquid
`gamma_("app") =gamma_l-gamma_S`
`gamma_L=gamma_("app")+gamma_S`
Where `gamma_S` is coefficient of volume expansion for solid vessel. When liquid is placed in copper vessel
`gamma_L=C+gamma_("copper")` ..(i)
(As `gamma_("app")` for liquid in silver vessel =S)
From Eqs. (i) and (ii), we get `C+gamma_("copper")=S+gamma_("silver")`
`gamma_("silver")=C+gamma_("copper")-S`
Coefficient of volume expansion`=3xx` Coefficient of linear expansion
`impliesalpha_("silver")=(gamma_("silver"))/(3)=(C+gamma_("copper")-S)/(3)`.