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` ?

Explanation

Here the volume of air in the flask remains the same. This is only possible when the expansion of flask is exactly the same as the expansion of mercury in the flask.
Here coefficient of cubical expansion of glass is
`gamma_(g)=3alpha=3xx9xx10^(-6)=27xx10^(6).^(@)C^(-1)`
Here to keep the volume of aire in flask constant, we have
Expansion of flask `=` Expansion of mercury
`(1000)gamma_(g)DeltaT=x. gamma_(m)DeltaT`
[Let x be the volume of mercury in the flask]
or `x=V.(gamma_(g))/(=100xx(27x10^(-6))/(1.8xx10^(-4))=150cm^(3)`