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`

Answer

C

Explanation

Apparent coefficient of volume expansion for liquid
`gamma_(app)=gamma_(L)-gamma_(s)thereforegamma_(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)` forliquid in copper vesse=C)
When liquid is placed in silver vessel
`gamma_(L)=S+gamma_(silver)` ... (ii) (As `gamma_(app)` forliquid in silver vessel =S)
From Equation (i) and (ii), we get `C+gamma_(copper)=S+gamma_(silver)`
`thereforegamma_(Silver)=C+gamma_(copper)-S`
Coefficient of volume expansion `=3xx` Coefficient of linear expansion
`rArralpha_(silver)=(gamma_(silver))/(3)=(C+gamma_(copper)-S)/(3)`