《那些古怪又让人忧心的问题》第12期:摩尔鼹鼠

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MOLE OF MOLES

摩尔鼹鼠

Q. What would happen if you were to gather a mole (unit of measurement) of moles (the small furry critter) in one place?

Q.如果你把一摩尔的鼹鼠放到一起会发生什么? 8211;肖恩.赖斯

A. THINGS GET A BIT gruesome. First, some definitions.

A.有点可怕。首先我们要弄清一些定义。

A mole is a unit. It 8217;s not a typical unit, though. It 8217;s really just a number-like 8220;dozen 8221; or 8220;billion. 8221; If you have a mole of something, it means you have 602,214,129,000,000,000,000,000 of them (usually written 6.022 × 1023). It 8217;s such a big number1 because it 8217;s used for counting numbers of molecules, which there are a lot of.

摩尔是一个计量单位,而不是典型的那些单位。它其实就是一个数字,就像 8221;一打 8221;或 8221;十亿 8221;那样。如果你有1摩尔的某种东西,那么这意味着你有602214129000000000000000个(通常写成6.022×1023)这种东西。这个数字无比巨大2,因为它就是用来计算分子数的,而分子可是有许许多多的。

A mole is also a type of burrowing mammal. There are a handful of types of moles, and some of them are truly horrifying.2 So what would a mole of moles-602,214,129,000,000,000,000,000 animals-look like?

8220;Mole 8221;也可以指一种会打洞的哺乳生物:鼹鼠。鼹鼠的种类有许多,其中有一些看上去非常吓人。那么一摩尔(602214129000000000000000只)鼹鼠放到一起会是什么样的呢?

First, let 8217;s start with wild approximations. This is an example of what might go through my head before I even pick up a calculator, when I 8217;m just trying to get a sense of the quantities-the kind of calculation where 10, 1, and 0.1 are all close enough that we can consider them equal:

首先我们先从一些狂野的近似联想开始。很多时候我在拿起计算器进行计算之前,都会先在脑中想一想,这次就是一个例子,我想对这个数量有一个大致的概念。在这么大的数字面前,10和1与0.1之间的区别已经微乎其微,我们可以近似地把它们认为都是相等的。

A mole (the animal) is small enough for me to pick up and throw.[citation needed ] Anything I can throw weighs 1 pound. One pound is 1 kilogram. The number 602,214,129,000,000,000,000,000 looks about twice as long as a trillion, which means it 8217;s about a trillion trillion. I happen to remember that a trillion trillion kilograms is how much a planet weighs. . . . if anyone asks, I did not tell you it was okay to do math like this.

鼹鼠的体形很小,我可以很轻松地把它们拿起来再扔出去。任何我能扔出去的东西重量都是1磅。1磅就是1千克。602214129000000000000000这个数字看起来有一万亿的2倍长,所以它大约有一亿亿亿这么多。我恰好记得一颗行星的质量也差不多是这么重。如果任何人提起这种计算方法,千万别说是我教你的。

That 8217;s enough to tell us that we 8217;re talking about a pile of moles on the scale of a planet. It 8217;s a pretty rough estimate, since it could be off by a factor of thousands in either direction.

这也就意味着1摩尔鼹鼠的大小已经能和行星的大小相媲美了。这个估算相当粗略,可能多算或者少算了几千倍。

Let 8217;s get some better numbers.

让我们用一些精确些的数字。

An eastern mole (Scalopus aquaticus) weighs about 75 grams, which means a mole of moles weighs:

一只东部鼹鼠(拉丁学名:Scalopus aquaticus)重约75克,也就是说一摩尔的鼹鼠重:

That 8217;s a little over half the mass of our moon.

这比半个月球还要重一些。

Mammals are largely water. A kilogram of water takes up a liter of volume, so if the moles weigh 4.52 × 1022 kilograms, they take up about 4.52 × 1022 liters of volume. You might notice that we 8217;re ignoring the pockets of space between the moles. In a moment, you 8217;ll see why.

哺乳生物体内很大一部分是水。1千克的水体积为1立方米,所以那么多的鼹鼠的体积大约为4.52×1022立方米。你可能发现了我们这里忽略了鼹鼠间的空隙,稍后你就会知道为什么要这么做。

The cube root of 4.52 × 1022 liters is 3562 kilometers, which means we 8217;re talking about a sphere with a radius of 2210 kilometers, or a cube 2213 miles on each edge.

4.52×1022立方米的立方根是3562千米,也就意味着这么多鼹鼠能堆成半径2210千米的一个球,或边长2213英里(1英里≈1.6千米)的立方体。

If these moles were released onto the Earth 8217;s surface, they 8217;d fill it up to 80 kilometers deep-just about to the (former) edge of space: This smothering ocean of high-pressure meat would wipe out most life on the planet, which could-to reddit 8217;s horror-threaten the integrity of the DNS system. So doing this on Earth is definitely not an option.

果这些鼹鼠被释放到地球表面,它们堆起来能够达到80千米高,差不多已经到了(之前定义的)外太空的最低高度。这个吓人的高压肉柱会抹掉这个星球上绝大多数的生命,这会威胁到域名解析系统的完整性,所以在地球上这么干是万万不行的。

Instead, let 8217;s gather the moles in interplanetary space. Gravitational attraction would pull them into a sphere. Meat doesn 8217;t compress very well, so it would undergo only a little bit of gravitational contraction, and we 8217;d end up with a mole planet slightly larger than the Moon.

相反,我们可以把鼹鼠都堆在星际空间中。在重力的作用下,它们会慢慢聚集成一个球体。肉不怎么能被压缩,所以这个大肉球只会因重力作用而缩小一点,最后我们将看到一个比月球稍大一些的鼹鼠星。

The moles would have a surface gravity of about one-sixteenth of Earth 8217;s-similar to that of Pluto. The planet would start off uniformly lukewarm-probably a bit over room temperature-and the gravitational contraction would heat the deep interior by a handful of degrees.

鼹鼠星表面的重力加速度约为地球的十六分之一,和冥王星差不多。起初整个星球的温度都很均匀,差不多比室温高一些,随后重力收缩会使内部的温度上升几摄氏度。

But this is where it gets weird.

之后事情就变得奇怪起来。

The mole planet would be a giant sphere of meat. It would have a lot of latent energy (there are enough calories in the mole planet to support the Earth 8217;s current population for 30 billion years). Normally, when organic matter decomposes, it releases much of that energy as heat. But throughout the majority of the planet 8217;s interior, the pressure would be over 100 megapascals, which is high enough to kill all bacteria and sterilize the mole remains-leaving no microorganisms to break down the mole tissue.

鼹鼠星说白了就是一个大肉球,其中蕴含着巨大的能量(鼹鼠星所含的卡路里足够目前全世界人口吃上300亿年)。一般来说,有机物被微生物分解时,会以热量的形式释放出大部分蕴藏的能量。但鼹鼠星大部分内核的压强在100兆帕以上,这么高的压强足以杀死任何细菌,并把鼹鼠的尸体都蒸熟。这样鼹鼠体内就不存在可以分解鼹鼠肉的微生物了。

Closer to the surface, where the pressure would be lower, there would be another obstacle to decomposition-the interior of a mole planet would be low in oxygen. Without oxygen, the usual decomposition couldn 8217;t happen, and the only bacteria that would be able to break down the moles would be those that don 8217;t require oxygen. While inefficient, this anaerobic decomposition can unlock quite a bit of heat. If continued unchecked, it would heat the planet to a boil.

在接近表面的地方,压强没有这么高,但还需要面临另一个难题:鼹鼠星的内部含氧量非常低。没有氧气,普通的分解过程将无法发生,只有那些厌氧菌才能在这种条件下继续分解。虽然厌氧分解效率很低,但这个过程仍会释放大量热量。这股热量最终会把整个星球都变成一个大蒸笼。

But the decomposition would be self-limiting. Few bacteria can survive at temperatures above about 60°C, so as the temperature went up, the bacteria would die off, and the decomposition would slow. Throughout the planet, the mole bodies would gradually break down into kerogen, a mush of organic matter that would-if the planet were hotter-eventually form oil.

但分解产物又会反过来限制分解的继续进行。很少有细菌能在超过60℃的环境里存活,因而随着温度的上升,细菌逐渐死去,分解进程也就慢慢停滞下来。整个星球的鼹鼠尸体会渐渐变成富含有机质的油母岩。如果星球的温度继续升高的话,它们最终会变成石油。

The outer surface of the planet would radiate heat into space and freeze. Because the moles form a literal fur coat, when frozen they would insulate the interior of the planet and slow the loss of heat to space. However, the flow of heat in the liquid interior would be dominated by convection. Plumes of hot meat and bubbles of trapped gases like methane-along with the air from the lungs of the deceased moles-would periodically rise through the mole crust and erupt volcanically from the surface, a geyser of death blasting mole bodies free of the planet.

鼹鼠星的外表面会向外辐射热量并冻结起来,冰冻的外壳就像给整个星球穿了一件毛大衣一样,会把星球内部和外太空隔绝开来,因而会减缓热量向外太空流失的速度。然而在液体内部,热传递的主要形式为对流,滚烫的肉浆和像甲烷(以及死去的鼹鼠肺中的空气)这样被困在其中的气体形成的气泡会在鼹鼠星的地壳里周期性地翻滚上来,从地表猛烈喷发出来并形成 8221;死亡 8221;间歇泉,将无数鼹鼠的尸体抛射出鼹鼠星球。

Eventually, after centuries or millennia of turmoil, the planet would calm and cool enough that it would begin to freeze all the way through. The deep interior would be under such high pressure that as it cooled, the water would crystallize out into exotic forms of ice such as ice III and ice V, and eventually ice II and ice IX.4

在经过数百万年的动荡之后,鼹鼠星开始慢慢停息下来,温度也低到整个星球都开始冰冻起来。此时由于鼹鼠星内部深处的压强如此之大,以至于在冷却的过程中,水结晶成了奇特的冰III和冰V形态,最终这些冰块都会变成冰II和冰IX形态。

All told, this is a pretty bleak picture. Fortunately, there 8217;s a better approach.

总而言之,这个故事的结局相当凄凉。不过好在有一个更好的结局。

I don 8217;t have any reliable numbers for global mole population (or small mammal biomass in general), but we 8217;ll take a shot in the dark and estimate that there are at least a few dozen mice, rats, voles, and other small mammals for every human.

我手上没有全球鼹鼠数量(或者小型哺乳生物的总体生物质量)的可靠的数字,但我们不妨认为小鼠、大鼠、田鼠以及其他小型哺乳动物的数量约为世界总人口的几十倍

There might be a billion habitable planets in our galaxy. If we colonized them, we 8217;d certainly bring mice and rats with us. If just one in a hundred were populated with small mammals in numbers similar to Earth 8217;s, after a few million years-not long, in evolutionary time-the total number that have ever lived would surpass Avogadro 8217;s number.

10亿颗宜居星球。如果我们将来去殖民这些星球,几乎一定会带着一些小鼠或大鼠。如果这些星球中有百分之一住着和地球上数目相当的小型哺乳生物,那么几百万年后(相对于整个宇宙的进化史来说已经很短了),所有曾经存活的这些小生物的个数将会超过阿伏伽德罗常数。

If you want a mole of moles, build a spaceship.

所以如果你想要有一摩尔的鼹鼠,得先造一艘宇宙飞船。

8220;One mole 8221; is close to the number of atoms in a gram of hydrogen. It 8217;s also, by chance, a decent ballpark guess for the number of grains of sand on Earth.

一立方英里约等于4π/3立方千米,因而半径为X千米的球的体积和边长为X英里的立方体的体积几乎一样。英文mole的两个含义分别是摩尔(计量单位)、鼹鼠。

That 8217;s a neat coincidence I 8217;ve never noticed before 8211; a cubic mile happens to be almost exactly 3π cubic kilometers, so a sphere with a radius of X kilometers has the same volume as a cube that 8217;s X miles on each side.

这里有一个我以前从来没注意到的巧合:一摩尔的数量接近于一克氢中所含的氢原子数。地球上所有的沙粒的数目也恰好很接近这个数字。

No relation.

相互之间没有关系。

标签:   发布日期:2024-03-09 06:32:00  投稿会员:Aucao