You can mix 10 marbles until they sort themselves. Why not 100?

Corrections and FAQ in this comment! 0) If you want to see the ink machine ideo about turbulent and laminar flow in a tube: https://www.youtube.com/watch?v=qm5AHAb0SmY and if you just want to watch it go, I have a 45 minute single cut: https://www.youtube.com/watch?v=DtYVYfOvgKE 1) I'm a little loose with the definitions when I get to the interchangeability of entropy and energy, but that's because it gets really complicated in a hurry - maybe a topic for a future video. What I'm referring to is "thermodynamic free energy", which is not conserved like "real" energy. If you have a bucket of water on a ladder and you let the water pour out of it into a bathtub, you could extract energy from that process with a paddlewheel or something - that's "free energy" being spent. Once the water lands in the bathtub, the kinetic energy of it falling goes into heating the water, so now the energy of the water is in heat, and there's nowhere to put the waterwheel, so the energy, although it's still there, is kinda useless. Entropy is exchangeable with "thermodynamic free energy", not "real energy". 2) 5:05 "proobability" 3) When talking about osmosis, I intentionally swept enthalpy of mixing under the rug. there are other (real, non-entropic) forces that can increase osmotic pressure in certain cases en.wikipedia.org/wiki/Enthalpy_of_mixing 4) my “push the marbles to one side” demo may LOOK like the classic “maxwell’s demon” hypothetical, but it’s supposed to represent what’s actually happening near a REAL semi-permeable membrane. I think the ideal “demon” would not produce osmotic pressure, but even in this demo of 20 marbles, there was some measurable osmotic pressure 5)

Matt Parker would have filmed coin flip attempts until he got 10 tails in a row, then just casually throw the footage in without further comment.

The three laws of thermodynamics: 1. You can't win. 2. You can't break even. 3. You can't even quit the game.

As a Physics TA this is absolutely GOD tier Physics education. You've perfectly communicated the basics of undergrad-level Statistical mechanics and Thermodynamics and given a solid foundation for the rest of the math and equations without using ANY Jargon. Like Einstein said, if you cant teach it to a 6 year old you don't understand it well enough.

Imagine the ink in the water system shot out and the ink cloud spelled out “Entropy, pfft” and then dissipated- but the camera broke.

I like to use this example when someone says “well it’s possible.” For an extremely extremely unlikely event. “Yes, it is possible, it is also possible for every molecule of oxygen in the room to shift up 6 feet, but I’m not about to spend my whole life standing on chairs to avoid suffocating.”

There is a consequence of entropy we deal with in our day-to-day lives at the macroscopic level: tangled wires. There are so many configurations where wires are tangled compared to the few configurations where they're neatly separated that they have a tendency to become tangled with the energy input from random jostling.

So you're telling me there is a chance?

As a biologist I'd never really looked in to why osmosis happens just knew that if different concentrations of fluids are separated by semi permeable membranes it occurs, thanks for showing me why

Dude is actually Maxwell's demon with balls.

I LOVE the overall explanation, but I have a little nitpick about the sugar/water example: At sufficiently high sugar concentrations, statistics is not the only force driving the dilution, but energy (mixing enthalpy) will be released by changing the intermolecular interactions between sugar and water (there will be "free" water instead of only "hydration shell" water touching other "hydration shell" water). By chance we actually produced a physically-chemically better, albeit less tangible, example, when decommissioning an NMR magnet a few months ago: We closed the helium pressure sensing line at the magnet cryostat, but left the pressure sensor at the other end connected. Because the line (plastic hose) was more permeable to helium than to air (as most things tend to be), the pressure inside the hose actually decreased by some 200 mbar below ambient pressure over a few weeks. Helium diffusion from the inside to the outside was more likely than the other way round due to the concentration gradient, and air diffusion in the other direction was hindered by the material of the hose. However, there are no relevant interactions between the different gases that would contribute to this, at least not at the pressures and temperatures we are talking here.

This made me think of another way of explaining why a systems entropy increases with the coinflips : If you have a random system of coins, lets say 6 head and 4 tails, and you have to randomly pick one coin to flip, you are more likely to pick a coin showing head since there are more of them, then when you flip that coin, you can either land on head and nothing changes, or land on tails and entropy increases. This makes it clear why any system tends to entropy. In your example at 9:16 you flip all the coins at once instead of picking one at random to flip which made it less clear to me why it would tend to increased entropy. Thanks for another great video :)

I guess a non circular way of phrasing the second law is "physical distributions of things will resemble statistical distributions, and those distributions get narrow if you have enough things"

This is why production of industrial chemicals often runs at high temperatures and pressures, often in a gas phase. It's basically to beat unfavorable chemical equilibria... Sometimes heat is used just to speed things up if the product formation is thermodynamically favourable but kinetically unfavourable. The product is often continually separated from the reaction mixture to keep its concentration low which favors more production as the system continually approaches chemical equilibrium. One of the oldest of such processes is the production of quicklime in a lime kiln. Here calcium carbonate is roasted at high temperatures give off carbon dioxide, leaving behind highly reactive calcium oxide melt used for making cements. The quicklime "wants" to turn back into calcium hydroxide or carbonate once it cools down, because different conditions favor different products. This is why it's so hard to make pure chemicals, especially organics - sometimes it's super tricky to separate a single compound and this explains why 98% purity costs $10, 99.9% purity costs $100 and 99.99% purity costs $10,000+

As a high school physics teacher I am often frustrated by poor explanations or loose definitions of entropy. This is outstanding! You have explained it in a way that non-physics students can understand. This is extremely helpful for understanding biological systems, heat transfer and the universe in general.

i feel like alpha phoenix has gone from "applied science" channel to a more "steve mould" type explainer. im here for it

This is so cool, I have never really considered that "entropy always increases" is not as much a physical law as just a restatement of the law of large numbers in an unbounded universe.

5:30 I love that you KNOW there are thermodynamicists watching...

Oh cool. So "Do you know why is it hard for things to be 'in order'? It's not because it's hard, it's actually because it's very improbable!"

12:30 this is a great visualization why it's /theoretically/ possible to throw a tennisball at a brickwall and have it quantum tunnel through. But the /chance/ that every single particle of the ball dodges every single particle of the wall in it's path is less likely than the ink reversing out of it's "spike". 14:30 I was already wondering why osmosis filtering requires pressure to work. Now I know. Because without the pressure, the water would "prefer" to become dirtier instead of cleaner.