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为何雨滴在数学上是不可能的 – 译学馆
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为何雨滴在数学上是不可能的

Why Raindrops Are Mathematically Impossible

在这个年代还有很多物理研究在雨滴:凝聚力,附着力,空气阻力。
There’s lots of physics going on in raindrops: cohesion, adhesion, air resistance – I
我意思是,雨滴下降通常看起来更像柔弱无害的泪滴。
mean, falling raindrops often look more like jellyfish than teardrops – but perhaps most
但是最令人着迷的是雨滴中看似不可能的物理疑问。
fascinating is the physics that makes raindrops impossible.
你可能认为下雨滴很简单普通。
You might think making a raindrop is easy – just cool water vapor in the air past
只是在空气中冷却水蒸汽到达了它的凝结点而已,对吧?
its condensation point, and it condenses into liquid droplets, right? But there’s a big
但是还有一个大疑问存在。基本上,在表面的水滴本身。
problem standing, almost literally, in the way: the surface of the droplets themselves.
液体很讨厌变成水滴。
Liquids hate surfaces – they’re bound by the laws of intermolecular attraction to pull
它们被分子间引力的法则所束缚,试图将它们的表面尺寸减小到最小。
together in an attempt to minimize the size of their surfaces. That’s why small water
这就是为什么小水滴是球形的,为什么你能把大量的水放在一个便士的原因。
droplets are spherical, why you can put a huge amount of water on a penny, and why bubbles
这就是为什么泡沫可以形成的夸张的造型的原因。
form the crazy shapes they do.
科学的说法是,表面需要更多的自由能量来维持他的空间结构。
The technical way of saying this is that surfaces require more free energy to make than volumes.
举个栗子!当你把冷凝饱和的空气,从气体变成液体时,
For example, when you’re condensing water in saturated air from a gas to a liquid, every
每个立方厘米的水,你能释放能量只是从其体积和压强变化的能量。
cubic centimeter VOLUME of water you make releases energy just from its change of volume
释放的能量大概足以把一个苹果弹到一米多高吧。
and pressure – roughly enough to lift an apple a meter into the air. But to make each
平方厘米的表面的水需要输入一个能量。
square centimeter of the SURFACE of that water requires an INPUT of energy – not much,
但这相当于举起一笔财富1厘米的财富数字。
but it’s equivalent to lifting a fortune cookie fortune 1 centimeter.
大量的水啊,从能量到体积方面。
For large amounts of water, the energy you get from the volume, which is proportional
这是成比例的半径的立方,足以弥补由于表面能量消耗面积正比于半径的平方。
to the radius cubed, is more than enough to make up for the energy cost due to the surface
体力的测量往往使体积更大的符合条件。
area, which is proportional to the radius squared. Cubing tends to make things bigger
但是对于很小半径的,相反的才是真的。
than squaring. BUT for really small radii, the opposite is true – cubing a small number
测量的体积是一个小数字,使它小于面积平方。
makes it smaller than squaring it. This unavoidable mathematical truth means that if a water droplet
这不可避免的数学真理意味着如果一个水滴低于一定规模,然后让它需要更多的能量比表面积更大。
is below a certain size, then making it bigger requires more surface area energy than is
从体积到能量释放,这意味着它需要能量的液滴堆积。
released from volume energy, meaning it TAKES energy for the droplet to grow, so it doesn’t
所以水滴不缩小,对于纯粹的立方和二次函数来说,这等值相当于其2/3。
– it shrinks. For pure cubic and quadratic functions, this equivalence point happens
这是当 x³ 开始变得比 x² 快时,但是在水滴中大约有几百万分子。
at 2/3 – that’s when x^3 starts growing faster than x^2, but for water droplets it’s
随机聚集的太多,虽然还不到宇宙的年龄!
somewhere around a few million molecules; way too many to randomly clump together in
因此,雨滴在数学表达上是不可能精确的,
less than the age of the universe! And thus, raindrops are impossible for the precise mathematical
对于小数目,事实上 x² 增长速度比 x³ 快。
fact that x squared grows faster than x cubed – for small numbers.
好吧,雨滴是这么明显的存在,但是如果你想知道如何避开二次和三次曲线之间的冲突。
Ok, so obviously raindrops exist, but if you want to know HOW they sidestep this battle
如果你感兴趣,你可以去看《分钟地球》的视频《雨滴从哪来?》
between quadratics and cubics, you’ll have to go watch MinuteEarth’s video about how
PS:感谢你的观看!
raindrops form.

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