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A one litre flask contains some mercury....

A one litre flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains tha same. What is the volume of mercury in the flask? Given the cofficients of linear expansion of glass is `9xx10^(-6)//^(@)C` and the coefficient of volume expansion of mercury is `1.8xx10^(-4)//^(@)C`

Text Solution

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Since the colume above mercury remains the same at all temperatures, the expansion of the glass vessel must be the same as that of mercury in the vessel. Also `gamma_g=3alpha_g=27xx10^(-6)//^(@)C`. Let V be the volume of the mercury. Then , from `DeltaV=VgammaDeltaT`
`Vxx(1.8xx10^-4)xxDeltaT=10^-3xx27xx10^-6DeltaT`
`(because L=10^-3m^3` and `gamma=3alpha`) or `V=150xx10^-6m^3`
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