Temperature Tension
Why can a filled cup of water hold fewer quarters when it is warm?
The scenario that we begin with is simple. A glass of water is filled to the brim. We can slowly drop quarters into the water. Despite the cup being completely filled, the water will not spill over, at least for the first few quarters. However, we notice that if the water is heated up, the amount of quarters we can add until the inevitable spill is less. For example, take a look at Figure 1.
Both cups are approximately identical, filled to the brim with water. The water in the cup on the left is filled with room temperature water. On the other hand, the right-side cup is filled with hot water. One by one, I dropped quarters into each cup until the water spilled over. Take a minute to watch the video in Figure 1. The water in the hot cup spilled over first, after only 6 quarters. After this, it took 7 more quarters in the room-temperature cup for it to spill over. All in all, it took the hot cup only about half the number of quarters as compared to the room-temperature cup in order for a spillover. Today's article will explain why this happens. We'll begin by talking about the surface tension of water.
Figure 1
Figure 2
In a mathematical sense, surface tension is the tendency of liquids at rest to pull themselves together to take the shape with the least surface area. For our situation, when the water begins to come over the brim of the cup, the water has two options. It can either pull apart and fall off, or stay together at the top of the cup, which will keep its surface area minimized. Obviously, the water will hold together and push over the rim of the cup as shown in Figure 2. Looking back at our original question, both the hot and room-temperature cups acted in this way. They continued to rise until the surface tension was no longer strong enough to hold the water together. It follows that for warmer temperature liquids, the surface area must be weaker.
To understand why surface tension is weaker at warmer temperatures, we must zoom in to see what's going on. In water, the molecules are all attracted to each other. This happens because water is formed with 2 Hydrogen and 1 Oxygen atom. In H2O, the hydrogen atoms are negatively charged while the oxygen atom is positively charged. Coulomb's law for electricity defines that oppositely charged atoms will be attracted to each other. Therefore, each oxygen atom of a water molecule will be attracted to another water molecule's hydrogen atom.
However, inside the bulk of the water, this has no real effect. Take a look at Figure 3. The water molecule at the bottom is surrounded by other water molecules. As a result, attractive forces pull from every side and they all cancel each other out. However, if we look at the water molecules at the very surface, this no longer holds. The water molecules at the surface will be pulled in any direction where there are other water molecules. The difference between the surface and bulk water molecules is that at the surface, there is no upward attraction. As a result, the net attraction is downward towards the rest of the water. This is another explanation for why the water doesn't spill above the brim. Even though gravity pulls the surface of the water off the cup, the water tries to stay together because of surface tension.
Finally, we can talk about temperature. Temperature is merely a definition of the average speed of molecules. When water is warmer, H2O molecules are speeding around much faster. When the molecules are moving quickly, the electrical attraction between molecules is harder to form. This explains why the warmer water experienced a weaker surface tension.
Figure 3