A container of capacity 700 mL is filled with two immiscible liquids of volume 200 mL and 500 mL with respective volume expansivities as `1.4xx10^-5//^(@)C` and `2.1xx10^(-5)//^(@)C`. During the heating of the vessel, it is observed that neither any liquid overflows nor any empty space is created. The volume expansivity of the container is

Options

A. `1.9xx10^(-5)//^(@)C`
B. `1.9xx10^(-6)//^(@)C`
C. `1.6xx10^(-5)//^(@)C`
D. `1.6xx10^(-6)//^(@)C`

Answer

A

Explanation

The increase in volumes of the two liquids due to an increase in temperature `DeltaT` will be
`DeltaV_1=V_1gamma_1DeltaT`
and `DeltaV_2=V_2gamma_2DeltaT`
`:.` Total volume expansion
`DeltaV_1+DeltaV_2=(V_1gamma_1+V_2gamma_2)DeltaT)`
The average increase in volume per unit volume per degree rise in temperature will be
`((DeltaV_1+DeltaV_2))/((V_1+V_2)DeltaT)`
`gamma=(V_1gamma_1+V_2gamma_2)/(V_1+V_2)` ..(i)
But since the cubical expansion of the two liquids compensates that of the container `gamma` for the container will be given by Eq. (i)
`gamma=(200xx1.4xx10^-5+500xx2.1xx10^-5)/(200+50)`
`=1.9xx10^(-5)//^@C`