# 英语煎蛋小学堂视频百科118：雨滴在数学上是不存在的(MP3+中英双语)

cocotang 于2015-08-06发布 l 已有人浏览

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There's lots of physics going on in raindrops:cohesion,adhesion,air resistance-I mean,falling raindrops often look more like jellyfish than teardrops-but perhaps most fascinating is the physics that makes raindrops impossible.You might think making a raindrop is easy just cool water vapor in the air past its condensation point,and it condenses into liquid droplelts,right?

But there's a big problem standing,almost literally,in the way:the surface of the droplets themselves.Liquids hate surfaces they're bound by the laws of intermolecular attraction to pull together in an attempt to minimize the size of their surfaces.That's why small water droplets are spherical,why you can put a huge amount of water on a penny,and why bubbles form the crazy shapes they do.

The technical way of saying this is that surfaces require more free energy to make than volumes.For example,when you're condensing water in saturated air from a gas to a liquid,every cubic centimeter volume of water you make releases energy just from its change of volume and pressure,But to make each square centimeter of the surface of that water requires an input of energy not much,but it's equivalent to lifting a fortune cookie fortune 1  centimeter.

For large amounts of water,the energy you get from the volume,which is proportional to the radius cubed,is more than enough to make up for the energy cost due to the surface area,which is proportional to the radius squared.Cubing tends to make things bigger than squaring.But for really small radii,the opposite is true cubing a small number makes it smaller than squaring it.

This unavoidable mathematical truth means that if a water droplet is below a certain size,then making it bigger requires more surface area energy than is released from volume energy,meaning it takes energy for the droplet to grow,so it doesn't-it shrinks.

For pure cubic and quadratic functions,this equivalence point happens at 2/3 that's when x^3 starts growing faster than x^2,but for water droplets it's somewhere around a few million molecules;way too many to randomly clump together in less than the age of the universe!

And thus,raindrops are impossible for the precise mathematical fact that x squared grows faster than x cubed-for small numbers.Ok,so obviously raindrops exist,but if you want to know low they sidestep this battle between quadratics and cubics,you'll have to go watch Minute Earth's video about how raindrops form.

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