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A long cylindrical metal vessel, having ...

A long cylindrical metal vessel, having a linear coefficient `(alpha)`, is filled with a liquid upto a certain level. On heating it, it is found that the height of liquid column in the cylinder remains the same. What is the volume coefficient of expansion of the liquid?

Text Solution

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Volume of liquid V = al , Increase in volume `Delta V = (Delta A) l (therefore l ` is constant )
`implies V gamma _(l) Delta T = (2 alpha) A.l Delta T implies V gamma _(l) DeltaT = 2 alpha V Delta T`
`therefore V = Delta l implies gamma _(l) =2 alpha `
`implies `VOlume coefficiet of expansion of liquid `= 2 alpha`
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