The Mysterious Entropic Force

entropy is not disorder for example this Beaker of dice has less entropy than this Beaker of dice and this box of nails has less entropy than this box of nails let me show you why this is by first starting with a bunch of disorganized dice in a jar normally to get stuff to pack down better you have to tap it tapping works great for spheres but not for cubes for cubes you have to twist them if you suddenly start and stop the jar the sheer force from the jar allows the dice to rotate until their flat surface is facing down over many starts and stops a pattern emerges amazingly from this seemingly random jiggling of the dice they all line up in nicely stacked rows and columns perfectly fitting into the most packed way they could fit into this jar this will actually happen with any solid particle of any regular shape if I take a box of nails for example and Shake it for a while eventually they all align shake a bunch of hard Spears and they'll organize into a face centered cubic pattern all hard particles will tend to spontaneously organize themselves it seems like there's some Force making these shapes align in a certain way but why well it's because of something called directional entropic forces it's when entropy itself acts like a force these cubes and nails are going from a low entropy state of looking all disorganized to a higher entropy state of looking organized now if you thought that entropy was disorder you aren't alone if you ask most people which jar has less entropy they'll probably tell you that the one that's nicely ordered has less entropy in fact let's check chat GPT which can represent most people I guess so I'll ask it if I have a jar that has a bunch of randomly oriented Dice and a jar that has a bunch of dice nicely stacked in rows and columns which one has more entropy the jar with the randomly oriented dice has more entropy compared to the jar with dice stacked in rows and columns the lack of order and the high degree of Random mean the system is highly disordered which corresponds to high entropy at first thought this seems right indeed chat GPT is a little bit right the orientational entropy of the system decreases but this loss in entropy is way more than offset by a huge increase in translational entropy of the system what I mean by this is that when the dice are disordered they take up this amount of volume but once the dice are ordered and you look at the same volume you can see that there's this new amount of free volume that opens up this makes it so that the amount of free volume per D increases so if we wanted we have all this space above for any Dy to move anywhere it wants and when we increase the number of places that a Dy can be it means that we've given the whole system more possible states that it could be in and entropy is defined as the number of possible states of a system so the entropy increases so any solid shape has a tendency to maximize face to-face alignment this creates more free volume and that means that overall the entropy is greater in an ordered versus a disordered box of shapes of the same volume so in this case entropy acted like this unseen Force pulling the dice together to fit into this tightly packed pattern as close as possible this mysterious force is called the entropic force it's an emergent force that happens from the statistical tendency for every system to increase in entropy over time this entrop I force feels and acts like a true force in fact when I stretch out this rubber band the reason it Springs back isn't due to any elastic Force pulling it back it's just due to the entropic force let me show you what I mean if I just take a single molecule of atoms strung out in a line like this there are no other forces acting on them other than the fact that they're connected to each other and they're jiggling around like atoms do they're free to move and fold in any direction but if I disconnect this and here look what happens to the string of atoms they shoot to the other side and curl up there isn't some Force that's making them coil together like this it's just that statistically there are more ways to be in a coiled State than a straight state if we wait long enough sometimes randomly it'll pop out straight again for a split second but overall there's overwhelmingly more ways to be in a coiled State than in a straight State and since everything always tends to move towards the state that has more possible configurations the string of atoms coil together even if I pull it and stretch it out again it Springs back like a rubber band in fact I have to exert a force to even get it straight again the relationship between this force and the entropy of the molecule is given by this equation here Force equals temperature times the change in entropy divided by the change in distance or length that we stretched it out so this emergent Force happens purely from the fact that entropy increases over time this is the same thing that's happening in a rubber band there are these long polymer molecules that are coiled right now but when I pull on the rubber band it straightens them it takes Force to do this and if I let it go it Springs back purely from the entropic force in fact anytime you have the movement of matter with increasing entropy then there's this entropic Force so don't be tempted to call entropy disorder think of it more as a tendency to move towards more possible configurations or States before we continue if you like learning from my channel then you'll love mellan TV mellan TV provides the best documentaries ad free I really like the space genre on here where I just watched an awesome documentary about Venus but there are so many cool genres that you'll love as well mellan TV's motto is television worth watching and I 100% agree with that so if you want to try out mellan TV today you can scan the QR code or click the link in the description box to start your free trial today now let's get back to our experience I also want to make a little caveat to what I said about things ordering even though in this case the entropy of the ordered system was higher than when it was disordered that isn't always the case for example in many crystals the entropy of the crystals after Crystal formation is less than before but this is because when forming the crystal heat was released so overall the entropy still increased so if ever there are little pockets of decreased entropy like when I air condition my garage that means that somewhere else like outside of my garage I'm increasing the entropy this tendency for entropy to increase is universal in fact it's so Universal that we call it a law the law is that the entropy of the universe is always increasing with time we call it the second law of Thermodynamics what's amazing is that this is a law simply because of a statistical effect when enough chaotic and random events happen eventually it leads to very predictable events like when I pull an elastic band I know it's going to spring back ow [Music] [Music]

Channel: The Action Lab

Views: 39,602

Keywords: second law of thermodynamics, dice, entropy, the action lab

Id: LBRBB6D8SdY

Length: 7min 24sec (444 seconds)

Published: Fri Jun 21 2024