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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

Verified by Experts

KEY IDEA
We know that both vessel the liquid expand , and they will expand in such a manner that the difference of their volumes will remain unchanged or in other words the expansion of mercury will be equal to that of the whole flask .
Calculations : If V is the volume of flask , `V_L` is volume of mercury and `V_A` is volume of air in it , then
`V=V_L+V_A`
As with the change in temperature , volume of air remains constant , the expansion of mercury will be equal to that of the whole flask , that is
`DeltaV=DeltaV_L`
or `Vgamma_GDeltatheta =V_Lgamma_LDeltatheta` ( as `DeltaV=Vgamma Deltatheta`)
Here `V=1,L=1000 "cc" and gamma_G=3alpha_G=27xx10^(-6)//""^@C` . So ,
`V_L=(1000xx27xx10^(-6)//1.8xx10^(-4))`
= 150 cc .
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