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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 teardropsbut 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 droplets, right? But there’s a big

• problem standing, almost literally, in the way: the surface of the droplets themselves.

• Liquids hate surfacesthe liquid is 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 youre 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 pressureroughly enough to lift an apple a meter into the air. But to make each

• square centimeter of the SURFACE of that water requires an INPUT of energynot 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 cubedfor small numbers.

• Ok, so obviously raindrops exist, but if you want to know HOW they sidestep this battle

• between quadratics and cubics, youll have to go watch MinuteEarth’s video about how

• raindrops form.

There’s lots of physics going on in raindrops: cohesion, adhesion, air resistance – I

B2 中高級 美國腔 雨滴 次方 體積 能量 表面積 製造

# 為什麼製造雨滴是不可能的 (Why Raindrops Are Mathematically Impossible)

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bsofade 發佈於 2016 年 07 月 14 日