A glass bulb contains air and mercury. What fraction of the bulb must be occupied by mercury if the volume of air in the bulb is to remain constant at all temperatures? The coefficient of linear expansion of glass is `9xx10^(-6)//K`.

Options

A. `(3)/(20)`
B. `(3)/(2)`
C. `(5)/(20)`
D. `(1)/(2)`

Answer

A

Explanation

Volume of the space above the mercury will remain constant if increase in volume of the vessel if equal to the increase in the volume of the mercury for any increase in temperature. Let V' be the volume of mercury and V the volume of the vessel.
Then `Vxx27xx10^-6xxDeltaT=V' xx1.8xx10^-4DeltaT`
or `(V')/(V)=(27xx10^-6)/(1.8xx10^-4)=(3)/(20)`