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