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Density of mercury at 15^(@)C is 13.56g*...

Density of mercury at `15^(@)C` is `13.56g*cm^(-3)` and its coefficient of real expansion is `18 times 10^(-5@)C^(-1).` What will be the mass of `600cm^(3)` of mercury at `130^(@)C`? What will be the volume of 600 g of mercury at `130^(@)C`?

Text Solution

Verified by Experts

We know, `rho_(2)=rho_(1)[1-gamma(t_(2)-t_(1))]`
Here density of mercury at `15^(@)C, rho_(15)=13.56g*cm^(-3)`
Coefficient of real expansion, `gamma=18 times 10^(-5@)C^(-1),t_(1)=15^(@)C " and " t_(2)=130^(@)C`
Increase in temperature, `t=130-15=115^(@)C`
`therefore` Density of mercury at `130^(@)C,`
`rho_(130)=rho_(15)/(1+gammat)=13.56/(1+18 times 115 times 10^(-5))=13.285g*cm^(-3)`
`therefore` Mass of 600 `cm^(3)` of mercury at `130^(@)C`
`=600 times 13.285=7971g`
Volume of 600 g of mercury at `130^(@)C`
`=600/13.285=45.163cm^(3)`.
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