The apparent coefficients of volume expansion of a liquid when heated filled in vessel A and B of identical volumes, are found to be `gamma_(1)` and `gamma_(2)` respectively. If `alpha_(1)` be the coefficient of liner expansion for A, then what will be the be the coefficient of linear expansion for B? (True expansion - vessel expansion = app.exp)

Options

A. `(gamma_(1)-gamma_(2))/(3)+alpha_(1)`
B. `(gamma_(2)-gamma_(1))/(3)+alpha_(1)`
C. `(gamma_(2)-gamma_(1))/(3)-alpha_(1)`
D. `(gamma_(1)-gamma_(2))/(3)+alpha_(1)`

Answer

A

Explanation

Let V=Volume of liquid
`DeltaT="rise in temp"`
`V" "gamma_(1)DeltaT=VgammaDeltaT+V3alpha_(1)DeltaT` For (A)
`gamma_(1)=gamma+3alpha_(1)" "....(1)`
So, for `B" "gamma_(2)=gamma+3alpha_(2)" "....(2)`
Subtracting we get `alpha_(2)=(gamma_(2)-gamma_(1))/(3)+alpha_(1)`