Two identical containers X and Y are connected at the bottom by a thin tube of negligible volume. The tube has a valve in it, as shown in the figure. Initially container X has a liquid filled up to height h in it and container Y is empty. When the valve is opened, both containers have equal amount of liquid in equilibrium. If the initial (before the valve is opened) potential energy of the liquid is P1 and the final potential energy is P2 then :
Concept:
- Potential energy is the energy possessed by a liquid by virtue of its height above the ground level.
- If m is the mass of the liquid at a height h from the ground level, the potential energy of the liquid = mgh
Calculation:
Given, when the valve is closed then the height of the liquid is h
Let the total mass of the liquid is m,
Then the initial (before the valve is opened) potential energy of the liquid is,
P1 = mgh
Now when the valve is open then the total mass remains same and equal to m, and height of the liquid h' = \(\frac 12\)h
Then the final potential energy is,
P2 = mg\(\frac 12\)h
⇒ P2 = \(\frac 12\)P1
⇒ P1 = 2P2
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