The apparent coefficient of expansion of a liquid when heated, filled in vessel A and B of identical volumes, is found to be `gamma_1` and `gamma_2`, respectively. If `alpha_1` be the linear expansivity of A then that of B will be

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

B

Explanation

Let V be the volume of the liquid and `DeltaT` the rise in temperature Since apparent expansion`=`true expansion`-`expansion of vessel
`Vgamma_1DeltaT=VgammaDeltaT+V(3alpha_1)DeltaT`
or `gamma_1=gamma+3alpha_1` .(i)
and `gamma_2=gamma+3alpha_2` .(ii)
Where `gamma` is the coefficient of real expansion of the liquid. Substracting Eq. (ii) from Eq. (i)
`gamma_1-gamma_2=3(alpha_1-alpha_2)`
or `alpha_1-alpha_2=((gamma_1-gamma_2))/(3)`
or, `alpha_2=[(gamma_1-gamma_2)//3]+alpha_1`
Hence, correct option is (b).