A glass bulb contains air and mercury. If the volume of air in bulb is to remain constant at all temperature then the fraction of the volume of the bulb that must be occupied by mercury is `x/20`. Find out the value of 'x' (cofficient of linear epansion of glass `9xx10^(-6)K^(-1)`, coefficient of volume expansion of mercury is `1.8xx10^(-4) K^(-1)`)

Answer

3

Explanation

`V_(bulb)-V_("mercury")`
`=V_(b)(1+3alpha_(b) DeltaT)-Vm(1+gamma_(M)DeltaT)`
`rArr 3alpha_(b)V_(b)DeltaT =VmgammaMDeltaT`
`(V_(m))/(V_(b))=x/20 =(3alpha_(b))/(gammaM)`
`rArr x=(60xx9xx10^(-5))/(1.8xx10^(-4)) =30 `