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A 1-L flask contains some mercury. It is...

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` ?

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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