Question

A 1-L flask contains some mercury. It is found that at different temperature, the volume of air inside the flask remains the same. What is the volume of mercury in the flask, given that the coefficient of linear expansion of glass`=9xx10^(-6)//^(@)C` and the coefficient of volume expansion of `Hg=1.8xx10^(-4)//^(@)C` ?

Answer 1

Let `V` : volume of flask =`1` litre
`V_(m)` : volume of mercury
Since with change in temperature, volume of air remains constant, the expansion of mercury will be equal th that of whole flask.
Expansion of mercury `DeltaV_(m)=V_(m)gammaDeltatheta`
Expansion of mercury `DeltaV_(g)=Vgamma_(g)Delta=V.3alpha_(g)Deltatheta`
`DeltaV_(m)=DeltaV_(g)`
`V_(m)gamma_(m)Deltatheta=V.3alpha_(g)Deltatheta`
`V_(m)xx1.8xx10^(-4)=1xx3xx9xx10^(-6)`
`V_(m)=0.15` litre .