Live from Orlando, Florida, it's theCUBE. Covering ServiceNow, Knowledge 17, brought to you by ServiceNow. We're back in Orlando, everybody, Dave Vellante with Jeff Frick. Michael Hovert is here, he's the Vice President of the Inspire program at ServiceNow, a program launched last year. Michael, good to see you again. Great to be back. Thank you gentlemen. It's been an awesome week. I saw you early. You and I were at the financial analyst meeting, which is always one of my favorites. You get the Kool-Aid injection, perhaps for what we're doing theCUBE. And you know, I love it because we go from the numbers, you know, you guys spice it up with a lot of the details in the business units, but then you get to talk to the customers that you really learned. So what's the, give us a summary of the week for you. Sure, it's been a fantastic week. So last year was my first experience with knowledge. Wow, what a difference a year makes in terms of scale, right? In terms of maturity of message and really the maturity of outcomes that our customers are talking about. So if you think about what Scott Mason from Novartis spoke about on day one of transforming everything about the way work is done and work moves through the enterprise to serve their patient and health outcomes and how we're enabling that across not just IT, but finance, HR facilities, or right after that's how Ashley Gaspard drove a great message around the end customer experience and taking potentially the creation of a trillion dollar market space of increased productivity that could be unleashed across their industrial customers by better enabling the way they do work and that we're helping GE Digital achieve that. Those are the types of outcomes that, we were not talking about at this event a few years ago and now it's not that we're talking about them, it's that our customers are talking about them. So Inspire, when you announced it, like about a year ago, right? You go all in when you do something like this so it's impressive to see how far you've come in a year, particularly the types of people you've been able to attract both inside the Inspire program but also the way in which you've been able to get customers to engage, which is not always easy. So maybe talk about sort of the talent that you've been able to attract and sort of how you've applied that talent. Sure, so one of the common questions I get is how much of the Inspire organization comes from existing portions of ServiceNow? Not very much, we've got a few folks that were already here at ServiceNow already with the type of mindset that we were looking for and with the history of skills and capabilities we were looking for. But mostly it is new hires, right? And they come from the customer, they come from a career of serving C-level executives or they come from other platform transformational companies that maybe have lost their edge a bit and they want to get back to a place that's really going all in, driving top line, driving customer experience versus maybe optimizing. And so that's where they've come from. And then we just have to find that 1% of customers that's up against either a great opportunity or a great crisis with the will and the power to say, I'm going to fix it, I'm going to get there, folks like Ashley, wow.  And it'll change their market cap value and through our role in it, it'll change our market cap value. And that's what we talked about at the financial realm this day together. Yeah, well, so some of the numbers were like mind boggling. ServiceNow is a very transparent company. It's something that Frank has always believed in. Scarpelli, I think, shared, it's about a $15 million investment. You guys hope to drive hundreds of millions of dollars in pipeline, but you were saying off camera that that's good, that's easy value to measure. Anybody can understand that, but there's other intangible value, which is perhaps even greater, right? I mean, like you said, if you have GE a senior person at GE up on stage and advocating, as the old saying, customer satisfaction is one thing, customer loyalty is everything. It seems like you've been able to engender that. Right, there's a phrase, and I don't know who to attribute it to, that says if you do a really good job, you'll tell everyone about it. If you do an excellent, amazing job, everyone will tell the world. Everyone else will tell the world. Everyone else will tell you about the job you did. And I feel like while we're making humble, we're just starting to bridge to that point where we're here in the feedback from the customers, from the coverage analysts that go and talk to our customers, that we're doing a pretty good job. We're doing a good to great job. I'm a sort of tongue-in-cheek this week. It's like, it inspires one of the best freebies in the business, but how do you manage demand? I mean, people must be lining up to get to tap the expertise that you guys have. Absolutely, so the psychology of this is pretty easy. First, you have to establish that this is something of value, then you have to state the fact that it has a certain amount of scarcity to it. And then when you couple that with the fact that, but for you, because of your special circumstance, your brand, your insight, your value, you are one of the few, one of the 1% that I'm going to give it to you for free. Demand is incalculable, right? So we are supply constrained in terms of cost to serve and capability from a talent perspective to serve. We're not demand constrained. We are supply constrained, which means we have to really bet on the right 1% of customers. Yeah, and you have to bet on those customers because they don't have any financial skin in the game other than the fact that, of course, they've invested in service now, but it's not like an incremental project that they're paying for. They have to be willing to participate at senior levels of their organization. Correct, and it does remove a whole bunch of things that slow down time to value by saying, we don't have statements of work. We don't have terms of conditions. We don't have scopes. We have a social contract, like you and I would. That says, success would be measured as this. Your role will be measured this way. Our role will be measured this way, and we're going to go all in. However, it has a huge, massive cost to you as a customer, and the more the senior you are in an organization, the larger the organization, the more they immediately see this, and often preempt me talking about it. They say it to me, which is I'm asking for the one resource you do not have the ability to create or procure more of, which is time from your most talented leaders and resources who know the current and future state of your business direction. And you give me that time from them. You're never getting that time back. So I better give you something hugely valuable in return for you sharing that scarcity of that resource with me. I remember I was reading an HBR article years ago, and it was how Gutfeel beats data-oriented analysis, and sort of Jack Welch was the poster child for that. My question is, when you present a customer with that value proposition that you just laid out, I mean, intuitively they might say, wow, okay, I'm all in, or do they go back and make a business case or sometimes both? I wouldn't say they make a decision as formal as a business case, but we do have a very open and transparent conversation, because you said that's a big part of who we are as our culture is a lot of transparency that says based upon that, that transfer of value, we're investing, you're investing, not directly monetarily, but through applying some of the scarcity of resources that we both have. What's the right level of investment for the desired return, right? And so when we team with customers, it can be anywhere from an hour-long conversation to shore up perspective and identify key risks where it can be through to three or four months. So depending upon really the type of return they're looking for, if they think they've got it mostly settled, they're mostly on a good path, they simply want one more external perspective to give them confidence and to instill us with a bit of accountability for our role in that, then it's not that big a cost and it's not that big a decision. It's that three to four month one that sitting with Ashley, sitting with Scott Mason, those folks, those are bigger decisions. And it ultimately comes down to how much do I trust you and how much do I respect your ability to deliver on what we're talking about. And it's very simple. How much do I trust you? How much do I respect you? So I'm just curious, how much of that goes into your selection criteria when you're deciding amongst the plethora of customers you could work with in projects within those customers, the kind of assessments that you're taking into account before you decide I'm going with option A versus option B, C, D, E all the way to Z? So we definitely have the combination of science and then gut feel, right? So we definitely have criteria by which we look at how important is this customer's problem to create innovation around? If we innovated for you and your manifestation of this problem, could we, would it help the other 99% of customers that we will not have the chance to meet with? That's a big indicator, right? The repeatability and scale of innovating in the area that you're asking us to innovate. That's science, right? The second being you and your personal brand as a leader, but also the company which you lead. How credible are you? And if you achieve an outcome, are you going from okay to good or are you going from good to great? And we want to be helping people always get to great, right? The bigger the transformation from where they are, the better, right? And if so, that has that kind of brand impact, that gets to be more of the gut feel. So it's kind of a combination of those two things. Okay, well, and you know, again, we were talking earlier about there's a lot of different ways to measure success. But at the end of the day, the numbers matter. And what I love about what's happening at service now is that customers can start small. I mean, I won't name names, but I've talked to many customers who have started on relatively small deals under, well under $100,000, you know? And now they're customers that are very large deals, well over a million, you've done a lot of deals over five million. And there's a long way to go. I feel like this company is just barely scratching the surface. I mean, it sounds kind of crazy for a billion dollar plus company, but you've got aspirations to get to four billion. John Donahoe the other day even said, well, you know, hey, why stop there? You know, we can see the potential for 10 billion. The market size is potentially there. You guys always couch that with safe harbor statements, et cetera. But the fundamentals are very good. A lot of tailwinds and the Inspire program is a catalyst for that type of deeper activity into these organizations. So I'll give you the sort of last word on Knowledge 17, you know, one year in and Inspire. Where do you want to go from here? Fantastic setup. Three thoughts. First, I've had no conversations in the last month with John Donahoe that were about getting to four billion dollars, right? So while it's a publicly traded company, we all are focused on consistent overachievement of the financial targets every 90 days. That is in every single part of our DNA and that's absolutely in John's DNA. However, we get the luxury and Inspire of being a part of that organism, a part of that entity that's also looking at the long game, also looking at the long-term outcome. And I can tell you it's much bigger numbers than that that we're working on. So I'll confirm that. The second thought is I'm so proud of what our customers, our internal stakeholders, and our team have done in the last year together as sort of our freshman class of customers, our freshman class of Inspire team members to create outcomes from delivering revenue to improving NPS to taking out costs to improving employee experience. I mean, these are board level issues that we are working on with some of the best brands in the world, right? And so I'm very, very happy and proud of what that is and very humbled to be a person who's in the chair to help drive that forward. And then the third question which is, so where does it all go next, right? It's absolutely keep doing more of the same, but continue maturing in two dimensions. One, let's make it an even lower investment from customers to figure this stuff out, right? So if you think about optimizing, can we get to just as good an answer in half as much time because we are doing a better job of understanding where the crucial decisions lie. So that's one next step is, could we talk about a year from now that what used to take two months of collaboration now takes a month? How valuable is that? Not just from the cost offset of the time we spend together, but you get to start executing on that idea and executing on that transformation one month closer. You never get that month back if it takes two months. So that's huge value to the customer. And so that's one area that we will go forward with is more efficiency, more optimization in how much effort it takes to get to the right questions and the optimal answers for those questions. And the second thing is, I consider those kind of silver bullets, silver bullets that let us go shoot transformation werewolves, right? Once we find those silver bullets and we've used them a couple times and we have killed the werewolves getting in the way of big, big transformation, our entire company and our entire partner ecosystem and even our practitioner community in the customer base, they all are hungry for learning how to to put those bullets in their arsenal as well. And so we're starting to do more and more of that this year, which allows us to move our entire company forward, move the 99% forward based upon what works for the 1%. Very service now, like answer Mike like I said. And to the numbers, success is not a function of the revenue in the market cap or a function of the success. And the success comes from the customers and the value that they're getting from the platform. Absolutely, you've got the service now, DNA in you. No, I mean, that's been very clear. And there are actually very few companies today that sort of live and breed that culture. So thanks very much for coming on theCUBE. It was always great to see you. It was fantastic, thank you. You're welcome. All right, keep it right there, buddy. We'll be back with our next guest right after this short break. What's the biggest disruption that you're?


We use microphones most of the time. Microphones are in AirPods, earphones, even in your mobile phones. And also you might have seen singers or podcasters recording in a studio, singing or speaking to a microphone. Whether you are plucking, drumming, singing or speaking, microphone creates a high quality audio. But how do these microphones work? That is something that we will explore in this video. All right, now there are different types of microphones and one thing common in all of the microphones is that it takes in sound waves which is also called a pressure wave. As it changes air pressure near its source, it takes in a pressure wave and changes it and changes it into electrical energy, something like a voltage signal. It is taking in variations in air pressure and changing it into electricity. All of the microphones do this and there are many types of microphones. There is dynamic, electric, condenser. They carry out the same process but with different methods. Here we will look into how condenser microphones change audio signal to an electrical signal. Let's briefly talk about its structure first and then the physics of it. So here we have a condenser microphone and inside of the microphone there is a metal ring. There is a metal ring with two metal plates attached at both the ends. One plate is called a diaphragm. This is a diaphragm. And the other that you cannot see here, it is on the other side, it is at the back. That is called a back plate. And these plates are mostly coated with gold because gold doesn't corrode. And this is how it looks like. Here you see the metal ring and this is a diaphragm. On the other side there is a back plate which is also a metal plate. Now let's look at a sectional view. Let's look at it from an angle. So for that let me make some space first. Okay, here we have a mic and here we have the metal ring at the top and this right here is the diaphragm. This is the back plate and both of the plates are connected to a battery. In between these plates there is an insulator that is usually air because air is an insulator. This setup now starts acting as a capacitor because you have one positive plate and you have one negative plate and there is an insulator, there's a dielectric between them. So this starts behaving like a capacitor. Now let's go back to the main process, the main function of a microphone. It converts one form of energy into another. Sound energy or variations in air pressure into electrical energy. How do we get electricity out of mechanical motion of air particles which produce sound? One thing that we can be certain of is that since the pressure of the air is varying, it is changing because of someone speaking into the mic. The final electrical signal that we are interested in should also vary and change right. We know that a sound wave can be plotted like you can plot pressure to distance, pressure versus distance and the plot could look somewhat like this. You will have points of very high pressure. These are compressions and you have points of negative pressure which are rear factions. So if the input audio signal is changing, the output electrical signal should also change right. Other than this, you would also want the pitch of your voice to be the same right. If someone has a heavy voice and they are speaking into the mic, when you hear your recording, you should be able to hear the same pitch right. The pitch should match and pitch is defined by the frequency. So that means the frequency of the electrical voltage signal should also be the same as the frequency of the sound wave coming in. We can increase the amplitude of the electrical signal later by running it across an amplifier. So we need not worry about the loudness for now. One thing that we can worry about is keeping the pitch same. So our voltage signal, electrical signal should kind of mimic or copy the audio signal coming in. It should have the same frequency and that means it will also vary just like the audio signal. Now the question is, how do we get the voltage changing? We know that if a capacitor is connected across a battery, it will start storing charge. There will be a plate with a positive charge, in this case the back plate. This is the back plate. This will have a positive charge and the diaphragm, the other plate that will have a negative charge. And in some time, it will get fully charged because of which a potential will develop across the capacitor. So maybe if we change the voltage of the capacitor at a certain frequency which matches the frequency of the audio signal, maybe our job might be done then. Now how can we change the voltage across the capacitor? We could change the amount of charge on these two plates and make the voltage change. But the voltage should mimic or copy the audio signal, right? It should have the same frequency at all times. How do we make the charge move instantaneously from one plate to other, exactly knowing the frequency of the coming sound so that we are able to change the voltage according to that, that seems difficult. That seems quite difficult. Instead of changing charge to change voltage, we can also change the capacitance itself, right? So what are the ways of doing that? Capacitance depends on just the physical characteristics of the plates. So it's area, the material between the plates and also the distance between the plates. Changing the material in between or the area would be a difficult task, right? No one is getting inside a mic to do that all the time. We can, however, change the distance between the plates. And turns out that is what happens. The diaphragm, this diaphragm that you see, it is extremely, extremely thin. So think that when the pressure wave, when the sound waves are coming in and when they strike it, it starts vibrating. When there's a compression, it is pushed inside and when there's a rear faction, it is kind of pulled outside. And how will that look? That could look somewhat like this. So let's say you have sound waves coming in from the left-hand side. And when there's a compression, it pushes the diaphragm inside. And when there's a rear faction, it pulls it outside. So constant sound waves coming in also vibrates a diaphragm according to that. When the diaphragm is pushed inside, the distance decreases. And we know that capacitance is epsilon not A divided by D. So nothing in the top is changing, but D is decreasing, which means the capacitance should increase. Okay, so this is great because now we know that capacitance can change. And it can change totally mimicking or copying the audio signal. But we wanted a varying voltage. Something that can be recorded. So if the capacitance is changing, then the voltage should also change, right? Because we know that Q, this is equal to C into V. There is one problem over here. If the capacitance increases, if this increases, then if there is just a capacitor and a battery in the circuit, the voltage across the capacitor will always be fixed. It is equal to the battery voltage. So VB, this is equal to the voltage across the capacitor. VB is the battery voltage. So when the capacitance increases, more charge gets stored on the plates and there is no change in the voltage. So if we are somehow able to make the charge fixed on both of these plates, then changing the capacitance will lead to the change in voltage, right? So for that, what we can do is we can add a huge amount of resistance over here. Something around one giga ohms or mega ohms. So this resistor, it will keep the charge on the plates constant. There won't be any movement of charge. Now when the capacitor increases, the charge is fixed and the voltage decreases so that their product is equal to the fixed charge on the plates. This means that now VB, this is no longer equal to VC. It is no longer equal to VC because VC has decreased, right? If capacitance has increased, the potential across the capacitor has decreased and if capacitance decreases, then the potential would increase. So if VC is decreasing, if it is decreasing, then there must be one another voltage drop so that the addition is still equal to the battery voltage. And that, and that is across the resistor, that is across the resistor. Then it becomes equal to the battery voltage. So for, for example, if let's say initially the voltage across the capacitor, which was equal to the battery voltage, and that was let's say 48 volts. When the capacitance has increased, some voltage decreased. So now let's say the voltage is 34, less than, less than 48. So the extra voltage drop that is coming from the resistor. There is some voltage drop across this resistance and in this case, that would be 14 specifically. And similarly, if the, if the capacitance decreased, then the voltage would increase, it would become more than 48, maybe, maybe 60. Then the voltage across the resistance would be minus, minus 12, it would switch polarity. But their addition always comes out to be equal to the battery voltage. So as the capacitance oscillates with the same frequency as that of the sound wave, that leads to voltage change again in with the same frequency. And this leads to a voltage drop across the resistor again with the same frequency, completely mimicking the input audio signal. And then this signal, finally, let's see how that looks like. This signal is read across the resistor that is then sent to the amplifier to increase the amplitude. And if there is a phase difference, that is also taken care of. All right, so that is how a condenser, and it is usually called a capacitor, that is how a capacitor microphone changes audio energy into electrical energy using capacitors. Sound waves strike the thin diaphragm, changing the capacitance of the capacitor, which leads to a change in voltage that leads to a voltage drop across the resistor, which is then recorded and sent to other components in the circuit.


Hey guys it's Tilly and today I'm back with another video. It is going to be my top 10 TBR books that I actually have on my bookshelves and for those of you who don't know I have a huge TBR that now takes up two entire bookshelves and it was really hard to just pick the top 10 because I just want to read them all but I have narrowed it down. These are the ones that I'm the most excited to read and that I will probably get around to reading soon. So in 10th place I have The Outliers by Kimly McCreith, McCryte, I don't know how to pronounce it but this book seems like it's going to be a really interesting mystery. So basically you have The Outliers which are people who can hear what is in everybody else's minds. So basically it says on the back here like imagine how valuable it would be, how much danger you would be in. And it goes up to talk about a girl called Wiley whose best friend Cassie has gone missing and then she starts to receive text messages that just are a bit out there and yeah so basically to me it sounds like it's going to be a really good mystery, hopefully action packed but I'm really intrigued by it so yeah I want to read it. This place we have Wolf by Wolf by Ryan Grodden and I haven't read this one yet because I really wanted to wait till the second book in the series came out before I read it because it sounds like a book that the ending will leave me wanting more and so I want to make sure that I actually have the more before I start reading it.  I don't really know what to expect from this book but I have heard really amazing things from it so I'm super excited plus I'm a huge fan of historical fictions so yeah. I've had this book on my shelf for a very long time and it has taken me just about that same time to realize that this is an author that I've already read before and it is in fact the Schwab and I did not connect the dots that this was the same author until like a few months ago so that is The Archived by Victoria Schwab and I am really excited to read this book. I have heard many great things about it one reason I haven't actually read out things because I haven't got the entire series and if it's a Victoria Schwab book then I know I'm going to love it anyway so I better buy those yeah more books. This next one is a new release and the cover of this book is so beautiful that I had to pick it up and that is The Loneliness of Distant Beings by Kate Ling and as you guys can see it's pretty damn beautiful. I love books that have stars on the covers especially like this kind so yeah I really want to read this. So from what it sounds like this is a sci-fi novel basically about a girl who's living on a ship she obviously dreams of like a bigger life than just traveling through space most importantly that she wants to feel the sun on her skin and then a new character called Dom comes into her life and suddenly her life revolves around him as if he is the son too so it sounds like it's going to be a romance but I really do hope there is more to it because I wouldn't mind like a real nice action packed romance. You know after reading Illuminae I think that's changed all sci-fi novels to me I just expect like crazy epicness to be happening in space all the time. Now why I've been putting off this next book um it's something that is right up my alley once again it's an author that I absolutely love and it sounds like it's gonna be a book that I will become my favorite and yet I have not read it and I've heard it there since like January I think and that is passenger by Alexander Bracken and I just don't know why I haven't read it yet. Thought it was about a girl who has pulled back three time I think to 1776 in the midst of a pirate sea battle and she has to kind of figure out how to live her life in this new time zone while also trying to get back and you know meeting people that makes her kind of wonder does she want to go home. It is a book that I know we're like and that is why it's like number six on my top pen list because I'm gonna read this. Ready Player One by Ernst Klein. This is another book that I have needed to read for a very long time but I've never got around to it and I'm not sure why. I'm pretty sure it's gonna be a movie though isn't it? I don't know I'll read it anyway. So what I've kind of got from the blow of this book is that the word that everyone lives in is pretty much destroyed. Everything has gone ugly. Think about Trump being president. This is what would happen afterwards and then you've got your main character and a lot of people who live in this world escape into virtual reality and so that's what this character does and there's like a big competition slash price to be won in his virtual reality and our main character here is trying to win that prize but it probably brings him trouble and dangers and love or some sort of wicked friendship that I'm hoping is in this book. The Art of Being Normal by Lisa Williamson and I have been looking at getting this book for a very long time. I only bought it last week because I haven't seen it on bookshelves like very often so when I did I picked it up straight away and I'm very excited to read it. So it is about two characters. You have David who wants to be a girl and Leo who wants to be invisible and basically David is getting bullied at school so Leo stands up for him and they create an awesome friendship which I really really hope that this book portrays really well because I'm in dire need of some really awesome friendship books right now and anyway pretty much they both have secrets and in a high school in this book you just know that the secrets aren't going to stay in so it's going to be probably very heartbreaking and hopefully uplifting at the same time. This is like my next go-to book when I'm in a bad mood because it's gonna be like an immediate cheer up book and that is the Trials of Apollo the Hidden Orochloric Warden and I'm pretty sure everyone knows what this book is about. It is about a polo, I love a polo and basically human posse go on an adventure. I don't actually know much besides that. I mean I've talked to a few people who have read it and everyone says it's good. Not as amazing as the other books but it's good but there's a polo in it and I love a polo so I'm pretty sure I'm gonna love this book and that is why it is number three. And number two is The List Endless by Carrie Firestone and I remember reading a bit about this book before it was released and it sounds like it's gonna be amazing and I looked online and the reviews were even better than I could have expected and so it's been pretty high in my TBR and I only managed to buy it last week and I need to read it very soon. So basically you have the main character who is called Maddie and she has her son planned out and then she finds that her grandma is dying and her grandma has decided that she's going to take the entire family on a round-the-world cruise and so they just go and have this huge adventure but there's also that heartbreaking undertone that the grandma won't be coming back with them, that this is her last hurrah pretty much but apparently it's just a really fun contemporary read that's filled with a lot of heart and I'm so excited. In first place is a book that I am so damn excited for. I only picked it up but I would be reading it right now if I wasn't happy to put it on the book and that is And I Darken by Kirsten White and I am so excited for this from what I have gathered it is a fantasy book this chick here is a beautiful warrior princess she also has her brother who is the opposite of her kind gentle and loving and then you also have the Sultan's son who is causing trouble for these two people so they're just trying to survive but she's also like ruthlessly going to do everything to make it out of this alive. Now this is what I'm getting at the blurb so I don't know if it's 100% accurate but the reviews I've heard of this and the people who have read it it is wonderful plus the hard cover for this book is beautiful which I need to go and buy a pronto because even I love this one the hard cover is so beautiful so I really hope that I enjoy it because then I can get multiple copies of it. So those are the books of the top 10 on my tbr if I have described any of them wrong I am truly sorry I'm sure I will amend for it when I have them in my wrap up videos for whenever I get around to reading them but for now I would love it if you guys could tell me your opinions on those books if you have read them that way I can maybe shuffle them around the piles to see what's good and what's not and yeah that'll be amazing. So thank you guys for watching I ha la la la sa ba da da ba cha. I will hopefully see you guys soon and until then I hope you guys have a fantastic week and everything great happens to you. Comment below what you guys are currently reading or say hello or make it have a nice little conversation and you guys can also talk to me on my other social media which I will link below. So yeah that's everything I will hopefully be back with another video soon I've kind of been a bit slow this like last two weeks so I'm going to be uploading just videos left right and centre until I'm back on track.


Welcome back to the next lecture on Statistical Thermodynamics. We have talked about beta, beta is equal to 1 over k T, where T is temperature on absolute scale. Today we will talk about negative temperature. What is the meaning of negative temperature? Is negative temperature possible? So, therefore, in order to discuss this we will also revisit the third law of thermodynamics a little bit. Let us get started. We will begin with talking about Boltzmann distribution. Remember that Boltzmann distribution or in other words fractional population of a state is given by n i upon n is equal to exponential minus beta E i upon q. Similarly, let us choose another state n j upon n is equal to exponential minus beta E j upon q. These are the expressions for the fractional population of i th and j th state for a system which has n number of molecules and the partition function is q. And if I now write the ratio n j upon n i it will be equal to n and n and q and q will get cancelled. So, I will have exponential minus beta E j minus E i. So, this way I can write the ratio of populations in a two level system I will now talk about in terms of temperature. So, the systems that we are talking about let us say 1 and 2. If I call this i th state I call it j th state I can also look at it this way that this is 0 of energy E 0 and this is separated at energy E. And now based upon what I have derived over here it is the ratio of the population of two states. And if I consider this two level system in which you have ground state and you have first on upper excited state at an energy E then how do I write the population? Consider again let us write down these two states. This is 0 this is E and let us say the population or number of molecules in the upper state is n plus and the lower state is n minus. Let us for the sake of convenience write like this. Then as we just discussed n plus divided by n minus is going to be exponential minus E upon k t. We just derived the expression for the ratio of populations in a two level system. Let us take a logarithm of this. If I take a logarithm of this I have log n plus n minus is equal to minus E upon k t. Let us consume negative sign. So, then I can write log n minus over n plus is equal to E upon k t. I have consumed minus sign and inverse this n plus and n minus. Let us rearrange for temperature. Now temperature from this is E upon k divided by log n minus over n plus. So, we have got an expression now for temperature which is equal to E by k divided by log n minus divided by n plus. Now you carefully look at this expression that we derived. That is if n plus is higher than n minus if n plus that means if we can contrive the population of the upper state to exceed that of the lower state n plus higher than n minus means somehow if we find out a way in which the population of the upper state exceeds that of the lower state that means in that case this term is negative and the temperature can be negative. So, according to this if we can devise a method in which the population of the upper state can exceed that of the lower state then the temperature must be negative. That means according to this if we consider this two level system then in such case the negative temperature is possible. Now let us discuss what is the meaning of this negative temperature that is temperature with a negative value. Remember we are not talking about temperature in degree Celsius. We are here talking about absolute temperature in Kelvin. What we are discussing here that if the upper state has more population than the lower state in a two level system then in that case the temperature has to be negative. Let us discuss further about this. So, what we have now all the statistical thermodynamic expressions that we have derived apply to t less than 0 as well as t greater than 0. What is the meaning of this comment? We have derived by now quite a few expressions thermodynamic expressions in a statistical connection partition function. We have derived expression for internal energy, we have derived expression for entropy and in each case we were able to connect these thermodynamic quantities or partition function with temperature and nowhere we mentioned that the temperature has to be positive or temperature has to be negative. That means all the statistical thermodynamic expressions that we have derived so far apply to both t less than 0 and t greater than 0. But we will now soon discuss that the meaning of those quantities how does it change when we apply to t greater than 0 or when we apply to t less than 0. Let us look at the next comment. The states with t less than 0 are not in thermal equilibrium. This is important to recognize the states with t less than 0 are not in thermal equilibrium and therefore have to be achieved by techniques that do not rely on equalization of temperatures of the system and its surroundings. So, these non thermal equilibrium states this is beyond the scope of current discussion you will study at higher level. But for the time being you assume or you believe that the states with less than 0 absolute temperature are not in thermal equilibrium and therefore different type of techniques will have to be used to achieve negative temperature. We will discuss very briefly about that. The third law of thermodynamics prohibits achievement of absolute 0 in a finite number of steps. This is a good time when we should revisit the third law of thermodynamics. The third law of thermodynamics says entropy of each substance is positive which may become 0 and it does become 0 at absolute 0 for perfectly crystalline substances. An alternate form of the third law of thermodynamics that we discussed in chemical thermodynamics was that it is impossible to achieve absolute 0 in a finite number of steps. And what is that? Let us take a quick look on that. This one is a plot of entropy versus temperature. At temperatures above 0 in general the entropy increases with rise in temperature. So, therefore if we consider the conditions where the sample is not subjected to any magnetization and the sample has lots of unpaired electron un magnetized whatever is its extent of unpaired electrons let us call it more disordered state. Now obviously when you subject this substance to magnetization that is you switch the magnetic field on there will be more orientation of electrons in the direction of applied field. So, therefore there will be more order it will be less disordered therefore entropy will be less and entropy temperature curve will behave like this. For the magnetized sample the entropy temperature curve will be lower than that for the un magnetized sample. Let us consider the process which is used to achieve very low temperature. Once again recalling the concepts that we developed in chemical thermodynamics that you can easily achieve for Kelvin because that is the boiling point of helium. And then when you pump helium through large diameter pipes and when the helium is pumped it will draw energy from the pipes and produce cooling. So, as I said if you pump helium through large diameter pipes you can bring down the temperature to 1 Kelvin. Now below 1 Kelvin what we need is adiabatic demagnetization and let us first talk in terms of electronic spins. Consider first that we have a sample for which the entropy temperature curve is blue 1 and we start with point A. At point A carry out isothermal magnetization process. Remember what I am saying is isothermal magnetization process. Isothermal means temperature should remain constant how will this temperature remain constant that helium will provide a link between the source and the sink. Extra energy which is liberated can be discarded or extra heat which is liberated can be discarded to the surroundings to the sink. So, when we carry out isothermal magnetization isothermal means it has to follow this horizontal line constant temperature. And when you carry out magnetization the corresponding point on the magnetized entropy temperature curve of the sample will be B. A to B it is isothermal magnetization. Next step is important. Next step ensure reversibility and now you remove the magnetic field very very very slowly in a reversible manner under adiabatic condition not what I am saying. Remove the magnetic field switch off the magnetic field very slowly in a reversible manner under adiabatic condition that is why this term adiabatic de magnetization is given. How now it will affect the thermodynamic quantities. Remember Clausius inequality what was that d s is greater than or equal to d q by t. And if I am ensuring reversibility that means d s is equal to d q reversible by t that is how we interpret this Clausius inequality that is the equality holds for reversibility. And if the process is reversible if it is adiabatic that means no heat is allowed to be exchanged between system and surrounding d q is equal to 0. If d q is equal to 0 d s is equal to 0 that means the process becomes isentropic the entropy does not change. So, therefore if the entropy does not change and you remove the magnetic field the entropy does not change that means it has to remain horizontal here horizontal behavior. The corresponding point on the un magnetized entropy temperature curve is c. Now again carefully examine what has happened from b to c is that the temperature has decreased there is cooling which has produced. So, what is done here is we need to have a paramagnetic material as we discussed here. We need a lot of electrons which are you know creating paramagnetic behavior and the sample of paramagnetic material can be d or f metal complex example is gadolinium sulphate octahydrate it will have lots of unpaired electron. And as I just mentioned first we cool to about 1 Kelvin that process I also discussed just now. And below all Kelvin what we need is adiabatic demagnetization process. We have just discussed one step first is isothermal magnetization second is adiabatic demagnetization. And in this sequence of two steps what we observe is the cooling has been produced. So, obviously now if we repeat these steps what will happen. If we repeat these steps let us say carry out again magnetization then adiabatic demagnetization another cooling will be produced then again magnetization demagnetization again cooling will be produced. That means we will keep on moving towards lower and lower temperature. What I have discussed over here is basically the spin of the electrons. This example also highlights the applications technological applications of the third law of thermodynamics. See how nicely this third law of thermodynamics is explaining the process of achieving very very low temperature. Why am I discussing this? Because we just discussed one highlight that according to third law of thermodynamics it is not possible to achieve absolute zero in finite number of steps. And if you look at here the number of steps that I will describe in the next slide that under what conditions in finite number of steps you can achieve zero whether those conditions are possible or not. But before that as I was talking to you that here we have used the electrons but the temperature lower temperature. So, what is the word of thermodynamics? World record minimum temperature achieved so far. The reported lowest temperature achieved so far is of the order of picocalvin 10 raise to the power minus 12 kelvin. The process that we are discussing is 4 kelvin liquid helium 1 kelvin pumping helium through large diameter pipes. Below 1 kelvin we are using the electronic magnetic movements. But the temperature of the order of picocalvin that I am talking about uses the nuclear magnetic movements that means the term there will be adiabatic nuclear demagnetization. Whether it is electronic demagnetization or it is nuclear demagnetization the process is same we need several cycles to lower the temperature. Now, let us talk about why it is not possible to achieve absolute zero in a finite number of steps. What is the other form of third law of thermodynamics is that entropy of every substance is positive I am repeating this which may become 0 and does become 0 at absolute 0 for perfectly crystalline substances. That means the entropy temperature curve have to merge at absolute 0. Now, this 0 is for the temperature scale not for the entropy scale. For entropy scale I will put 0 over here they are merging here some value which we are referring to as 0. And if you look at now the number of steps first step second step third step you keep on doing in order to achieve absolute 0 you need infinite number of steps. That is why the alternate form of third law of thermodynamics that it is not possible to achieve absolute 0 in finite number of steps. But if you look at the left hand side figure if the entropy temperature curve were to vary like this that they do not merge at absolute 0 then it is possible to achieve absolute 0 in finite number of steps. But then you are violating the third law of thermodynamics says that they must merge for perfectly crystalline substances. So, therefore, the right hand side figure suggests that it is not possible to achieve absolute 0 in a finite number of steps. No one has ever succeeded in cooling any system to absolute 0 and the reason for that we have just discussed. And the third law it is impossible to reach t equal to 0 in a finite number of steps. And that is what we were discussing over here we were at this highlight that the third law of thermodynamics prohibits the achievement of absolute 0 in a finite number of steps. Let us look at the next important highlight which says that however it is possible to circumvent this restriction in systems that have a finite number of levels or in systems that are effectively finite because they have such weak coupling to their surroundings. As I will soon show in the next lecture that it is possible to circumvent this restriction, but the systems chosen will be such that they have finite number of levels. For example, you know easiest one for us is to choose a two level system and then demonstrate. The practical realization of such a system is a group of spin half nuclei that have very long relaxation times. So, pulse techniques in NMR can achieve non equilibrium populations as can pumping procedures in laser technologies. So, these two methods that I have discussed over here we are not going to cover in this course you will study in the advanced level when you will learn NMR and pumping procedures in laser technologies there you will talk more about that. So, again emphasizing on that the expressions that we derived for example, for q in terms of temperature or u in terms of beta beta is essentially 1 over k t or s we have talked in terms of temperature and partition function which is essentially again described in terms of temperature. In the derivation of these equations we never said that these equations are not valid for t is equal to 0 or t less than 0. The expressions for q u and s are applicable both for t less than 0 and t greater than 0, but then what does it mean what is the meaning of negative temperature that we will discuss in the next lecture and how this negative temperature can affect the variation of partition function with temperature or variation of internal energy and entropy with temperature. We will discuss these in the next lecture. Thank you.


okay we're just walking out of five nights at freddy's this one's geared more towards teenagers someone let my kids tell you their thoughts it was okay at best okay at best yeah it was kind of weird yeah i don't know i don't know how to think about that what did you think of the look of the movie the robotic android type creatures were a little much they should have been creepier do you think it was scary no it was scary it was just like a little messed up if you think about it like kids getting kidnapped and i'm not gonna spoil it but yeah it was it was scary in some way there you have it really really intense concrete emotions going on i'll give you my thoughts on my channel so make sure to subscribe to hear those