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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 ?

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To solve the problem, we need to find the ratio of the heights of the liquid columns in two vessels containing liquids at different temperatures. We will use the concept of pressure balance and the coefficient of cubic expansion. ### Step-by-Step Solution: 1. **Understanding the Setup**: We have two vessels connected at the bottom by a thin pipe. One vessel contains liquid at \(20^\circ C\) and the other at \(80^\circ C\). The coefficient of cubic expansion of the liquid is given as \(\gamma = 10^{-3} \, K^{-1}\). 2. **Establishing Pressure Balance**: ...
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