字幕列表 影片播放
-
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 droplets, right? But there’s a big
-
problem standing, almost literally, in the way: the surface of the droplets themselves.
-
Liquids hate surfaces – the 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 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 – roughly 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 energy – not 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 cubed – for small numbers.
-
Ok, so obviously raindrops exist, but if you want to know HOW they sidestep this battle
-
between quadratics and cubics, you’ll have to go watch MinuteEarth’s video about how
-
raindrops form.
