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

    雨滴裡有許多物理學問:內聚力、附著力、空氣阻力

  • mean, falling raindrops often look more like jellyfish than teardropsbut perhaps most

    我的意思是:掉落的雨滴通常看起來更像水母而非眼淚,但也許最

  • fascinating is the physics that makes raindrops impossible.

    迷人之處在於無法製造雨滴的物理學

  • You might think making a raindrop is easy – just cool water vapor in the air past

    你可能會想說製造雨滴很簡單,就是冷卻空氣中的水蒸氣,過了

  • its condensation point, and it condenses into liquid droplets, right? But there’s a big

    它的凝結點,然後它就會凝結成液體水珠,對吧!但那有一個大

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

    問題,那就是水滴自身的表面

  • Liquids hate surfacesthe liquid is bound by the laws of intermolecular attraction to pull

    液體討厭表面,他們利用分子間吸引力來拉近彼此以

  • together in an attempt to minimize the size of their surfaces. That’s why small water

    試著減少它們的表面積,那就是為什麼小水珠

  • droplets are spherical, why you can put a huge amount of water on a penny, and why bubbles

    是球形,為什麼你可以放很多水在一個一分錢上,還有為什麼泡泡

  • form the crazy shapes they do.

    可以形成瘋狂的形狀

  • The technical way of saying this is that surfaces require more free energy to make than volumes.

    以專業的說法來說,這是因為表面比體積需要更多的自由能來形成

  • For example, when youre condensing water in saturated air from a gas to a liquid, every

    例如:當你正凝結飽和空氣中的水,使其從氣態轉換到液態時,每

  • cubic centimeter VOLUME of water you make releases energy just from its change of volume

    製造立方公分體積的水都會從它體積及壓力的改變來釋放能量

  • and pressureroughly enough to lift an apple a meter into the air. But to make each

    這大概足以舉一顆蘋果上升一公尺高,但要製造每一

  • square centimeter of the SURFACE of that water requires an INPUT of energynot much,

    平方公分表面積的水需要吸收一些能量,這不多

  • but it's equivalent to lifting a fortune cookie fortune 1 centimeter.

    但足以舉起一個幸運餅乾一公分高

  • For large amounts of water, the energy you get from the volume, which is proportional

    對大量的水而言,從體積獲得的能量正比於

  • to the radius cubed, is more than enough to make up for the energy cost due to the surface

    半徑三次方,這超過補充表面積能量損失

  • area, which is proportional to the radius squared. Cubing tends to make things bigger

    的二次方,立方往往大於

  • than squaring. BUT for really small radii, the opposite is true – cubing a small number

    平方,但對於非常小的半徑而言卻是相反的,將一個極小的數立方

  • makes it smaller than squaring it. This unavoidable mathematical truth means that if a water droplet

    會使它小於平方的值,這個數學結果表示如果一個水珠

  • is below a certain size, then making it bigger requires more surface area energy than is

    小於特定的尺寸時,那麼使其變大會需要更多的表面積能量,而這大於

  • released from volume energy, meaning it TAKES energy for the droplet to grow, so it doesn’t

    從體積所釋放的能量,這表示水珠花更多能量來變大,所以它

  • – it shrinks. For pure cubic and quadratic functions, this equivalence point happens

    會變小,對於純三次方和四次方的方程式而言,這個解發生

  • at 2/3 – that’s when x^3 starts growing faster than x^2, but for water droplets it’s

    在三分之二的時候,那正是x的三次方增加速度開始超越x的二次方的時候,但對於水滴,它

  • somewhere around a few million molecules; way too many to randomly clump together in

    周圍有百萬個分子;有太多途徑以至於不能隨機聚集在一起,在

  • less than the age of the universe! And thus, raindrops are impossible for the precise mathematical

    小於宇宙的年齡中!因此,雨滴不可能符合準確數學中

  • fact that x squared grows faster than x cubedfor small numbers.

    小數字的x平方會比x立方增加快速

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

    所以雨滴很明顯存在,但如果你想知道他們怎麼回避掉這場

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

    二次方與三次方的戰爭,那你就要去看地球一分鐘關於

  • raindrops form.

    雨滴如何形成的影片

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

雨滴裡有許多物理學問:內聚力、附著力、空氣阻力

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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
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