If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:13:27

Video transcript

the second law of thermodynamics tells us that the entropy of the universe is always increasing so the change in entropy when for the universe when it undergoes any process is always greater than or equal to zero and we showed in a previous video that it has a lot of implications it's you know if you define it well depend it's regardless of how you define your entropy whether you define entropy is equal to you know some constant times the natural log of the number of states your system could take on or whether you define and change in entropy to be equal to the heat added to the system divided by the temperature which is added either of these descriptions combined with our second law of thermodynamics tell us things like when you have a hot body next to a cold body so let's say this is t1 and this then I have t2 over here that heat will flow from the hot body to the cold body and we show that mathematically in the last video that heat will flow in this direction now one of the commenters on the last video said hey could you cover Maxwell's demon and and I and I will because it's it's it's a it's an interesting thought experiment that seems to defy this principle it seems to defy the second law of thermodynamics and it has a very tantalizing name Maxwell's demon apparently though it was not Maxwell who came up who called it a demon it was Kelvin all these guys you know they they they they're all they all metal and everything so Maxwell's demon so what's Maxwell's D and Max this is the same Maxwell famous for Maxwell's equations so he obviously dealt with a lot of things he's actually also the first person to ever generate a color image so Danny and this was in the mid 1800s so all around fairly sharp individual but what's Maxwell's demon so when we say something has a higher temperature than something else what are we saying we saying we're saying that it's average kinetic energy of its molecules bumping around here that the average kinetic energy of the molecules here is higher than the average kinetic energy of the molecules here none I said it's average kinetic energy and we've talked about this multiple times temperature is a macrostate we know that at the micro level all of these molecules have different velocities they're bumping into each other transferring momentum to each other you know this guy might be going super fast in that direction this guy might actually be going quite slow this guy might be going super fast like that that guy might be going quite slow it's just a hodgepodge of things you could actually draw a distribution if you knew the microstates or of everything you could you could actually draw a little histogram we could say okay for T 1 T 1 my average let's say this is on the Kelvin scale so you could say look my average temperature is here but I have a whole distribution of particles so let's say this is number of particles number of particles number of particles and I won't put a scale there you'll get the idea so I have a bunch of particles that are at T 1 but I have some particles that could be really close to absolute zero I mean it would be very few but it'd be very few and some numbers that and then you have a bunch that are maybe at T 1 and then you have a bunch of particles that could have actually kinetic energy higher than T 1 higher than the average kinetic energy maybe that's this one here maybe this guy down here is this guy with barely any kinetic energy maybe there's some guy who's almost completely stationary who's you know sitting right around there someplace so there's a whole distribution of particles likewise this T 2 system right here on average these molecules have a lower kinetic energy but you know there might be one particle here that has a really high kinetic energy and you know but most of them on average are lower so if I were to draw the distribution of T 2 my average is lower my average kinetic energy is lower but my distribution might look something like this it can't go backwards like that it might look something like this oh I don't know maybe it looks something like that let me try a little different I'll make it go just as high maybe it looks something like that right so notice there there are some molecules in T 1 that are below the average kinetic energy of T 2 right there are these molecules here these are these slow guys right there these are those slow guys and notice there are some guys in t2 that have a higher kinetic energy than the average in t1 so these are these guys right here these are these guys right here and so maybe so the fast guys in t2 so even though t2 is quote unquote colder it has lower average kinetic energy there are some molecules if you look at the micro Mac my microstate that are actually moving around quite rapidly and there are some molecules here that are moving around quite slowly so what Maxwell said is hey what if I had my and he actually didn't use the word demon but will use the word demon because it makes it seem very interesting and and and metaphysical on some level but it really isn't what if I had some dude let's call him the demon with a little trapdoor here let me draw it a little bit neater let me draw it a little bit neater so I have so between those two systems let's say let's say that they're insulated let's say that they're insulated they're separated from each other so this is t1 where I have a bunch of particles you know with their different kinetic energies and then here is t2 and I'm making them separated and maybe they're connected only by this little connection right here t2 these guys have a slower kinetic energy and what Maxwell his little thought experiment was hey let me say that I have some dude in charge of a door that's right here maybe the doors right here right and he has control over this door and whenever a really fast particle in t2 one of these particles over here come near the door so let's say this guy let's say this guy is flying let's say that guy right there yes he's going super fast he has super high kinetic energy and he's just going perfectly for the door so the demon says hey I see that guy he's coming for the door he's gonna lift the hatch he's gonna lift him his hatch and he's gonna allow this particle to get into that into t1 he's gonna allow that particle to get into t1 so after he lifts a hatch that particle will just keep going and it'll be in t1 and then when he sees a little and then he closes the hatch again cuz just wants the fast particles to go from t2 to t1 and then when he sees a little slow you know pokey little little particle coming here one of one of these guys down here he's like he opens a trap door again and he allows that one to go so then that guy shows up in here so if he just kept doing that what's it gonna look like at the end well at the end you're going to segregate and it could take a while but you're going to segregate all the slow particles on let me draw it I'll make the boundary and brown cuz now it's not clear which one is well we'll talk about a little bit so that's the boundary that's his door what's gonna happen at the end all the fast particles some of them are gonna be the original fast particles that are in t1 right there's some original fast particles in t1 are gonna be still on this side of the barrier but then all of the fast let me draw make sure you don't get these two confused um this is a separate picture now all of the fast particles from t2 are also gonna be stuck there cuz that you know eventually they're all gonna get close to that door if you wait long enough so then this guy is also gonna have a bunch of the uh what would originally in in the t2 side of the of the barrier they're also gonna be there so you're gonna have a bunch of fast particles likewise all the slow t2 particles are gonna be remaining on this side of the barrier so these are the slow guys and he's gonna he would have let all the slow t1 I shouldn't even call them t1 anymore that you know I call him side one side one particles here slow side one particles so what just happened here what just happened this was the hot body this was the cold body though the second law of thermodynamics would have told us that heat would have gone from here to here that their temperature should have equalized to a certain degree so the the hot body should get colder the cold body should get hotter they should kind of average out a little bit but using this this little demonic figure what did he do he made the hot body hotter right now the average kinetic energy here is even higher he transferred he transferred all of these high kinetic energy part to that distribution so now that distribution is going to look less you ad so the way you could think about if you transferred all of these guys to this guy over here the the distribution will now look something like let me see if I can do it it'll look something like that 41 instead of the old one and T 2 and he took all the hot ones away all the cold ones away from T 1 so these guys are gonna disappear they're not gonna be there anymore and he added them to t 2 he added them to t 2 so the distribution of T 2 is gonna look like that and he erased of course these from T 2 he took all of these guys out of t 2 let me erase this right here that was the old distribution of T 1 so the T 2 distribution now looks something like this now looks something like this so T 2 the at the new average it might be something like here so this is our my new T - and my new T 1 is gonna move to the right a little bit the average is gonna be high higher so this demon seems to have violated the second law of thermodynamics let me box off this right here cuz it's my little diagrams are overlapping this example shows that the hot got hotter and the cold got colder so you know Maxwell thought experiments hey we violated the second law of thermodynamics and this actually you know it this was a conundrum for many many years even and you know even in this century people kind of hey you know there's this something fudgy about here or something not quite right and the thing that's not quite right and I'm not gonna prove it to you mathematically is and it's kind of analogous to the refrigerator example is to have something here to have some dude some dude perhaps he's a demon here pulling this pulling this this this little door when it's convenient when you know the slope when the fast particles are going from this side or the slow particles going from that side in order for him to do it correctly he's gonna have to keep track of where all the particles are and you need to keep track of particles I mean these aren't these aren't balls like you know macro balls these are micro molecules or atoms he's gonna have to either you know he's gonna have to bounce light off of them or he's gonna have to bounce electrons microscope he's gonna have to keep track of these gazillion particles that are there and I mean think about there's a lot of he might you know he might have to have a super duper if it doesn't occur in his head he might have to have some kind of hard core computer microchip you know that's that's churning away and and this is this would be actually you know for a computer to do this this would be intensive computation power and let your computer run for a little bit and feel the microchip this is generating a lot of heat this is generating a lot of heat his his his his bouncing off light or whatever he's trying to bounce off off the off of the different molecules to be able to measure how fast they're going that's also going to generate heat he's gonna have to do work to do that he's you have to measure everything there's a lot of stuff that's going on that he's gonna have to do so the current answer is and it's it's not easy to prove mathematically but the current answer is if you actually wanted to build a demon like this and probably in our world today you would you'd use some type of computer with some type of sensors to attempt to do this and there are people who who are who have attempted to do this on some on some level this computer and this whole system is going to generate more entropy so this is going to the doubt the delta s here is gonna generate more entropy than the entropy that's lost by taking the the cold particles or by by making the cold side colder and the hot side hotter so Maxwell's demon I didn't do anything rigorous here I didn't prove it to you but Maxwell's demon it's an interesting thought experiment because it gives you a little bit more intuition about the different macro States and microstates and what happens at the molecular level in terms of temperature and how you can make a cold body colder and a hot body hotter but the answer is it really isn't a a paradox or anything like that that the the when you think about the the entropy of the entire system you have to include the demon himself and if you include the demon himself he's generating more entropy every time he opens that door and maybe there's some energy required to open the door itself but there's more energy required he generates more entropy when he does all of this than the entropy that might be gained than the entropy that might be lost when say for example one of these slowpoke particles kind of just traverses onto that side of the barrier anyway I thought I would just expose you to that because it's a really neat thought experiment so I'll see you in the next video