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# Lecture 25. Partition Functions.

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#### Automatisierte Medienanalyse

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Erkannte Entitäten
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that will be talking about was that NEC is that if you had a group assistance they can occupy different states the 1 that you see the most of what's going to dominate is the 1 that can be achieved in the most number of ways which intuitively sounds reasonable and further always said that if you have a really large system like say other gardeners number of molecules Neuralia see that dominate even more so it's a little abstract so I cooked up the full calculation here and what the calculation does is what we're doing is simple to state system there's 2 states has been tested by sort .period but instead of just looking at 1 point a bunch of times will say we have a box of quarters we shake the box of quotas and would take a peek inside and count the number there I had to tell us you we report the number as a percentage of fat right to expect 50 % heads so
that sort of thing now look good to the
regularly scheduled programming
with finding approximation for so on the Taylor series forever for even the ax is just 1 plus X was X squared over to was Cubillas over 6 races it follows that pattern but we're just going to take the 1st 2 terms in college good enough writers were really close to 0 and so we're going to do that and so 1st 2 terms this measure we take that exponential function right there it would just be 1 the mind is so we'll call the entire thing that to minus 2 beta not being not that entire thing contacts so they are not the 1st teachers would be 1 plus acts on our case 1 minus 2 major new not been so their our 1st 2 terms in the series and we're stop at 2 terms so that the distribute that minus sign in there then you get 1 ones the ones go away and you just left with 2 beta you not be right set approximation the numerator nothing that denominator will the same 10 cents thing take the 1st 2 terms so you can have 1 minus 2 patently not be not this time the ones positive to get 1 plus 1 equals 2 and then you subtract the 2 data not be enough I'm so now we can make even 1 more approximation because up top we said that made at times New not not riverbed is just 1 of Katie is really small it's much much less than 1 so that's true that was subtracted really tiny number from 2 well really care at 1 . 9 9 9 9 9 something or if it's too late which is considered to opposites it's so close to 2 soaring approximated being and then if you write that out with that with this faction this is what you get to the expectation value for the magnetic moment for this particular substance in wheat field at high temperature is just that you not squared Be not over take 4 times they have real estate so this is not a securities law this is known as Terri's Law and has a plot of it and that you know at high temperature populations tend equalized in this country confirms what we were thinking about just kind of a qualitatively rates its temperatures just kicking stifled tackles all over the place in a magnetic field is too weak to try and keep a maligned inaccuracy much of the net magnetic moment since we have the questions on the register blown through this stuff from unwanted fast and Israeli only back up will we get to the end with time left plenty of someone rehash of from the Northeast to attend
talks fast so I don't know I'm am
and find a partition function for this thing up as a 1st of all this is the energy we're talking about right the energetically they're all the same state is is there's only 3 different energetic states with they habit the did to generously and were looking at it again ,comma linear relationship between energy and number of contacts so the last context there are the higher energy you are so that's why we just come with a linear relationship here if you look at the coefficient funny not because 0 1 2 so but there's a partition function so looking at the ground status for different ways to make their ground state so the genesis for and where was called about energy level 0 so then you have the 2 0 which is 1 services for writers to generously 4 times in a 0 is 1 for the 2nd 1 is 11 ways to do it I and our function is the energy for that particular state is he not so it's easy to the minus the nite Tasmania and the last 1 is 21 ways to do it and energy but determined was that to unite sounds can be 21 times the to the minors how to unite times better all right so members for its petition functions of these smaller systems that we can actually write out a return partition function that typically things it too complicated for this attitude to get them although we can have this toy problems like we do ,comma mechanics to look at that and you can have a partition function of so it was with that we determined the average kinetic energy of the gas molecules and talk about translational energy right which is a really good way to describe energy those atomic gas right because Adams a considered points is as far as the mechanics of for the most part so I'm all your interest in his translational energy but you can have a gas like beginning can rotate rights then you have rotational partition functions as well so there's all kinds is British branches and come up with that the
pocket into college and so on equals 1 over Katie I prefer always used beta and Dr. Mott was saying this that makes experimentalist tend to favor 1 over Katie because temperatures on can actually you know to temperatures of more natural you know if you're running experiments and theory people tend to favor beta Smith -dash available arm so the ad and I think I just I have cultivated every time it's equivalent any really questions as we have almost a little over 5 minutes if there's anything you like me to do again but not in color today it's up to you france and the place if
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