Remember: do everything in moderation! That’s what the Pythagoras Cup teaches.
The Pythagoras Cup, also known as a Tantalus Cup, is named after Pythagoras. The same one with the right-angle triangles. It looks like a regular cup, except that it has a cylindrical protrusion in the middle of the cup. If you fill the cup halfway, nothing intesting happens. However, if you fill the cup up to a level near the top of the protrusion, the cup empties itself by leaking through the bottom. There are no secret levers or movable parts to this cup. So, how does it work?
A one-word answer to this is “siphoning”. A diagram of the cross section of the cup is below:
When the cup is about half-full, the level of liquid in the cup does not completely fill the inside of the cylinder. However, you raise the level of liquid in the cup, and the liquid completely fills the inside of the cylinder, the magic happens. The liquid siphons itself out of the cup through the bottom.
So, the only question that remains is how a siphon works and what the definition of a siphon actually is. You can use a siphon to move liquids from one container to another, through a tube, as long as the destination container is at a lower elevation than the source container. Below is a standard example of siphoning in action.
An interesting point to observe is that the liquid in the upper container first travels upwards against the pull of gravity before travelling downwards into the bottom container. This happens without a pump. The only thing that helps it along is gravity.
There are two theories as to why this happens. As the liquid falls down the vertical part of the tube to fill the bottom container, it creates a reduction in pressure near the top of the siphon, almost like a vacuum. As a result, the atmosphere is able to push against the liquid in the top container, causing it to fill the siphon, once more. This is the generally accepted explanation as to why the siphoning action occurs. However, you will find videos on YouTube showing that a siphon also works in a vacuum.
Of course, you can only do this under very controlled conditions, because liquids will evaporate in a vacuum. You have to ensure that the entire apparatus is completely clean. You also have to ensure the liquid is completely pure and free of any gas. They also “cheat” a little bit by using a very special liquid – an ionic liquid. You can think of ionic liquids as basic salts (an anion and a cation) that are liquids at a particular temperature, in this case, room temperature. Of course, these are fairly exotic compounds but they atoms have a very strong force of attraction between each other. In this scenario, another force takes over and provides the siphoning action – cohesion.
Cohesion can be thought of as the “stickiness” between molecules. Certain molecules are attracted to each other. In some compounds, such as water, this attraction is really strong, while in others, this attraction is weaker. Because of this force of cohesion between the molecules, the siphoning action can occur. As the molecules flow down the vertical tube, they are able to “pull” the molecules above them. This happens purely through their cohesive forces.
I would really like to go into more depth as to why certain compounds have high cohesive forces than others, but I do run the risk of boring you. So I’ll stop here!