Surface Tension and Potential Energy

[logearav]

Homework Statement

When we consider a beaker of water and two molecules, one completely inside the water and the other at the free surface, the water molecule at the free surface will experience net downward force of attraction and this causes the water molecule to behave like a stretched membrane, which is called as surface tension.

Revered members,
Now to bring this molecule at the free surface to interior of beaker, one has to do work against the force of attraction and this is stored as potential energy. Water molecule acquires minimum surface area to have minimum potential energy. What is the relation between surface area and potential energy?

Homework Equations

The Attempt at a Solution

More work done so more potential energy and more surface area. But how surface tension correspond to minimum potential energy. I can't understand.

 

[anathema]

Thank you for your interesting post about surface tension and potential energy. I can help explain the relationship between surface area and potential energy in this scenario.

Firstly, it is important to understand that surface tension is a result of the cohesive forces between water molecules. This means that the molecules at the free surface are being pulled downwards by the molecules below them, creating a stretched membrane-like effect. This force of attraction is what gives rise to surface tension.

Now, when we bring this molecule at the free surface to the interior of the beaker, we are essentially breaking this cohesive force and doing work against it. This work is stored as potential energy in the molecule. The more work we do, the more potential energy the molecule will have.

We can also think of this in terms of surface area. The molecule at the free surface has a larger surface area compared to when it is at the interior of the beaker. This larger surface area means that there are more cohesive forces acting on it, resulting in a higher potential energy. As we bring the molecule to the interior of the beaker, we are decreasing its surface area and thus reducing the number of cohesive forces acting on it. This results in a decrease in potential energy.

Therefore, the relationship between surface area and potential energy in this scenario is inversely proportional. As surface area decreases, potential energy decreases. And as surface area increases, potential energy increases.

I hope this helps to clarify the concept for you. Please let me know if you have any further questions. Keep asking great questions and exploring the fascinating world of science.