Question

A glass flask with volume 200 `cm^(3)` is filled to the brim with mercury at `20^(@)C`. How much mercury overflows when the temperature of the system is raised to `100^(@)C`? The coefficient of linear expansion of the glass is `0.40xx10^(-5)K^(-1)`. Cubical expansion of mercury `=18xx10^(-5)K^(-1)`.

Answer 1

The coefficienct of volume expansion for the glass is `gamma_("glass")=3alpha_("glass")=1.2xx10^(-5)K^(-1)`
The increase in volume of the glass flask is
`DeltaV_("glass")=gamma_("glass")V_(0)DeltaT`
`=(1.2xx10^(-5)K^(-1))(200cm^(3))(100^(@)C-20^(@)C)`
`=0.19cm^(3)`
The increase in volume of the mercury is
`DeltaV_("mercury")=gamma_("mercury")V_(0)DeltaT`
`=DeltaV_("mercury")=gamma_("mercury")V_(0)DeltaT`
`=(18xx10^(-5)K^(-1))(200cm^(3))(100^(@)C-20^(@)C)=2.9cm^(3)`
The volume of mercury that overflow is
`DeltaV_("mercury")-DeltaV_("glass")=2.7cm^(3)`