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Two vessels connected at the bottom by a...

Two vessels connected at the bottom by a thin pipe with a sliding plug contain liquid at `20^@C` and `80^@C` respectively. The coefficient of cubic expansion of liquid is `10^-3K^-1`. The raio of height of liquid columns in the vessel `(H_(20)//H_(80))` is nearest which interger ?

Text Solution

Verified by Experts

Because the sliding plug stays in the connecting pipe, the pressure in both the vessels at the level of the pipe must be the same.
`h_(20)d_(20)=h_(80)d_(80)`
`implies(h_(20))/(h_(80))=(d_(80))/(d_(20))`
`implies(d_0(1-80gamma))/(d_0(1-20gamma))=0.94`
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