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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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英语视频:煎蛋小学堂118:雨滴在数学上是不存在的,以幽默诙谐的方式为你解答那些那些你意想不到的科学小知识,含有中英双语字幕视频,mp3下载。
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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?

雨滴承受着许多物理作用:凝聚力,附着力,空气阻力 我是说 下落的雨滴与泪珠相比其实更像水母 但是 最有趣的是物理令“雨滴”不可能存在。你或许会认为雨滴很容易形成———只要让空气的水汽超过凝聚点,它就会凝聚成水滴 对吧?

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.

但这过程存在一个大问题。真实的大障碍:雨滴自身的表面。液体讨厌表面————它们被分子间吸引力束缚在一起 挤成一团尽量减少表面积。这就是小水滴之所以是球形的原因,硬币可以承住大量水的原因,也是泡沫形成这般疯狂形状的原因。

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.

从技术上来讲 与体积相比表面的形成需要更多的自由能。例如说 当饱和空气中的冷凝水从气态变为液体,每形成1立方厘米体积的水 释放的能量仅为它体积和压力的变化量 但每形成1平方厘米的表面积需要输入的能量 不算多 相当于举起一块幸运饼干1CM所需要的能量。

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.

对大量的水而言,体积减小释放的能量,与半径的三次方成正比,用来填补形成表面积所损耗的能量绰绰有余,形成表面积所损耗的能量为半径的平方。与面积相比体积更倾向于变大。但是对于极小的半径而言 就恰恰相反了 极小的数字 其三次方会比平方更小。

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.

这个躲不开的数学真理意味着 如果水滴小到一定程度,那么与体积所释放的能量相比它需要更多表面积能量,也就是说它需要吸收小水珠的能量增大体积,但这是不可能的 所以它会变小。

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!

纯就三次函数和二次函数而言,当量点位于2/3处 此时X3(立方)增长速度开始大于X2(平方) 但是对于水滴而言 这个点大约为几百万个水分子;随机聚集的方式非常多 都快赶上宇宙的年龄了!

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.

此外 对于精确的数学而言雨滴不可能存在的 因为对小数值而言X2(平方)的增长速度大于X3(立方)。但是事实上 雨滴确实是存在的,如果你想知道它们是如何避开平方和次方这个不可跨越的障碍,去看看之前的那期【雨滴的小秘密】。

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