Is there a definition that sets the limit as to what constitutes a “drop” of water? What is the smallest a drop can be before it just becomes a single molecule of H20?
And…if you took all the water on the entire planet and “stacked” it into a column that is one square inch in area, how tall would the column be?
The first question is too philosophical.
For the second question, Wikipedia says there is 321,000,000 cubic miles of water on Earth.
Each cubic mile contains (5280 x12) * (5280 x 12) * (5280 x 12) cubic inches, or 2.54 x 10^14 cubic inches.
Multiply this times the number of cubic miles of water, and get:
8.165 x 10^22 cubic inches of water on Earth
So a column 1 inch square would be 8.165 x 10^22 inches tall, or 1.288 x 10^18 miles.
That’s 13.8 billion times times the distance from the Earth to the Sun.
ETA: math error
For the first question, I recall that in science lab the standard was 20 drops to the milliliter.
drop size will vary with how the drop is created. a drop coming off a flat surface might be different from a tube. also will vary with tube size and tube characteristics. i don’t know if a drop has ever been defined.
A drop has indeed been defined, in several different measuring systems, in several different ways. Of course, these “standard drops” may actually correspond only very roughly to the size of actual drops, which, as has already been pointed out, can vary quite a lot for a variety of reasons.
Just to add to the list, I’d expect a significant variation with temperature as well.
I will try to find a cite, but I recall reading about an experiment that used either an electron or scanning probe microscope to answer your first question. IIRC they found that groups of water molecules behave like “drops” on a surface down to ~100 atoms. Not sure what kind of surface they used, I assume it was metallic.
I believe it’s a variation of the sorites paradox.
The ancient Greeks were a bright bunch in general but they sure did ask some retarded questions sometimes. A heap of sand stops being a heap when it stops heaping. It is as simple as that. Heaping is a collective property that doesn’t depend on any exact number of grains. A bunch of wet sand can be flat as a pancake and therefore not a heap whereas much less sand can heap quite well. It isn’t a discrete property however. Like physical attractiveness, there is a continuum of heapiness. I am not sure why they didn’t think of that.
The same is true for a drop of water. It stops being a drop when it loses the properties of a drop. A few molecules of water is just vapor. Two many molecules and it breaks apart when it falls. Drop your volume of water and see if behaves as a cohesive drop and there is your answer.
Take that bunch of wet sand and mold it into a heap.
So, wet sand flat as a pancake = “not a heap”
Wet sand molded into a pile = “heap”
At what point in molding that sand does it become a heap. There’s no point when it’s “sort of” a heap. It’s either a heap or it’s not. But can that point be defined?
Trying to generalize to a ‘continuum’ simply shifts the goalposts. It doesn’t address the central idea of the paradox at all.
That is the problem. It is a stupid paradox because it isn’t a real one. Take a person that most people find attractive like Brad Pitt. Start adding flaws one at a time, a small zit here, a scar there, a bump on the nose etc. Exactly how many flaws does it take to make him flip from attractive to butt ugly? That is the same “paradox” because attractiveness is a continuum just like heapiness is. It is just an English word for a concept.
Drop isn’t exactly the same thing however. Water will change its properties as more or less of it tries to share the same space. Given a perfectly stable environment and dispensing apparatus, the drops produced will be almost exactly the same size and can be measured experimentally. Volumes that are too large or small won’t have the properties of a drop at all.
But whether it’s considered to be a drop or not or a heap or not or attractive or not depends totally on the decision of the observer, reacting to their interpretation of the word.
Specific question: Can it be a heap if there are only 4 sand grains, and one is ballanced on top of the lower 3?
That is great once you have a concept like continuum. You have it thanks to the ancient Greek (and later) philosophers who worried about such problems and slowly (often over centuries) hammered out the concepts to deal with them. Sure it is not a problem once you know the answer, but just because it seems obvious to you now does not mean that that answer did not take a lot of hard intellectual work to find.
This isn’t a philosophical or scientific question, much less a paradox. It’s just definitional ambiguity. What does “big” mean? What does “wet” mean? It just changes depending on context.
Getting back to drops, since the OP extends a continuum down to a molecule of water, let’s make more generous the conventional usage of “drop” versus “droplet”, and ask how small a glob of water molecules can be and still have a collective nature.
Water droplets are quite small in clouds unless they are coalescing into falling raindrops. They exhibit an interesting behavior - there is, at any relative humidity greater than 100%, a droplet size that is at equilibrium with the air. Droplets larger than this equilibrium size will get bigger because condensation overwhelms evaporation, and droplets smaller than this size will get smaller because evaporation wins.
Droplets that are very small require quite a high relative humidity in order not to evaporate, and the smallest droplets of pure water evaporate extremely rapidly. Toward the end, as the droplet size approaches zero, the last few molecules practically explode apart, as opposed to individually getting jarred out of the still well defined surface of the drop. Typically, though, there are salts and other things in the droplet that become more and more concentrated as the drop evaporates, and then the question becomes whether deliquescence will capture more molecules versus letting them all desert the salt. Little particles of salt serve as condensation nuclei, if they form and then experience an increasing relative humidity (usually because the temperature drops).
If you get rid of the salt condensation nuclei, and keep increasing the relative humidity without any other particles around, at some point air ions themselves are able to nucleate condensation.
Cloud chambers are devices used in particle physics to make visible the paths of atomic particles as they trigger nucleation of droplets.
So, I think perhaps the answer most interesting in the light of the OP would be that the smallest clusters of water molecules that are not actually exploding from one another might be the best model of the smallest possible drop.
And where do you think you got fancy concepts like definitional ambiguity and context dependence from? Do you think caveman Ugg had them?
The words probably came up before organized, methodical philosophical/scientific inquiry?
If we had understood wavelength from the start, colors would probably be very different. Likewise, if we had understood molecules as cavemen, terms like “drop” would probably have been defined differently.
The question you meant to ask is really interesting and others are hammering it out. The question you did ask is easy. Two molecules of water.
Hate to break it to you, guys, but the OP doesn’t seem to care about the actual answer - he just wants to ask the question.
Words like continuum, definitional ambiguity and context dependence? No, no way.
But there is no way we could have understood these things “from the start” or “as cavemen”. It took millennia of both conceptual and technological development before they could be understood.