The volume of a glass vessel is 1000 cc at `20^@C`. What volume of mercury could be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are `1.8 xx 10^(-4 @)C^(-1)` respectively.

Explanation

Let volume of glass vessel at `20^(@)C` is `V_(g)` and volume of mercury at `20^(@)C is V_(m)`
so volume of remaining space is `=V_(g) - V_(m)`
It is given constant so that
`V_(g) - V_(m) =V'_(g) - V'_(m)`
where `V_(0)` and `V_(m)` are final volumes.
`V_(g) - V_(m) = V_(g) {1+gamma_(g) Delta theta} -V_(m) {1+gamma_(Hg) Delta theta} rArr V_(g) gamma_(g) = V_(m) gamma_(Hg)`
`rArr V_(m) = (100 xx 9 xx 10^(-6))/(1.8 xx 10^(-4)) rArr V_(m) = 50 c c`.