Most people get the right answer to the toothpaste puzzle, but it never ceases to surprise me how many get it wrong, and even staunchly argue their position. I’ve even seen it tested by taking a tube of toothpaste to the bottom of a swimming pool.
The question: What would happen if you took a tube of toothpaste to the bottom of the sea, and then opened it? It’s a great party question. Try it sometime.
Many people answer that the toothpaste would all squirt out. Some say ocean water would rush in. The right answer, as most of you surmise, is that nothing would happen. The wrong answer I hear most often is that the toothpaste would squirt out. Why? Because there’s so much more surface area on the tube than there is at the little opening — say 1 cm2 compared to 500 — so it would squirt out with 500× power, or something along those lines. Not true.
Some people ask if toothpaste is compressible, or if there are air bubbles inside the tube. Some suspect that if the toothpaste is squeezed and compressed in there, it would squirt out more vigorously, or they say that water would rush in to fill the vacated space. Both are wrong.
Toothpaste only moves from one environment (inside the tube) to another (outside the tube) when it’s in a high-pressure environment and there is a low-pressure environment nearby. At the bottom of the sea, there is one single pressure measurement (say 5 atmospheres, for example, depending on the depth) just as there is a single pressure measurement here on land (1 atmosphere). If the tube is in a 5 atmosphere environment, there is no reason the toothpaste would squirt out in order to reach another 5 atmosphere environment. This is where the argument of relative surface area between the nozzle and the tube comes into play. But it’s nonsensical. Choose any given 1 cm2 patch on a balloon; it does not pop at that point and all the air rushing out because there are so many other patches. The pressure from those other patches does not build up cumulatively. If it did, the same argument could be made for every single point on the balloon’s surface.
When we open and squeeze a tube of toothpaste, our squeeze is creating high pressure inside the tube. The toothpaste then vacates to the lower pressure environment outside the tube. Simple as that. At the bottom of the sea, there is no convenient low pressure region. So nothing would happen.
Discuss. I’m sure you will.