Now, this is the last kind or the fourth kind of processes found in a petroleum refinery, the supporting process. Interestingly enough, you will see that we also make a product here, the product that the refinery could sell a byproduct, if you will, to make revenue for the refinery. So, supporting processes make sure that the refinery could actually run. It's not a huge chemical conversion process, if you will, that have to do with making the desirable hydrocarbons. But the principle supporting process is the acid gas recovery and the sulfur recovery or acid gas removal and sulfur recovery. What is an acid gas? Well, H2S is the principle acid gas that is produced in the refinery from the hydro treatment processes. Remember, we remove sulfur from the fuels and from the fractions of crude oil as hydrogen sulfide. Hydrogen sulfide is an acidic gas, so it needs to be removed from the rest of the gases, typically methane, ethane that come with hydrogen sulfide to the recovery or the removal acid gas removal process that we use a basic solvent to capture the acid gas, particularly hydrogen sulfide. So it's essentially an acid-base interaction. We can use ethanolamine as a base in a solvent extraction process, a liquid extraction process to remove H2S, hydrogen sulfide from methane, ethane, other hydrocarbons that are not acidic. You will see that we also have some carbon dioxide that is found along with H2S, that's also an acidic gas that tends to be separated with hydrogen sulfide by solvent extraction in this basic solvent. So once H2S is captured or removed using the solvent extraction process, now we need to convert that into a soluble product. I know people always think that here is a point we could recover hydrogen for reuse hydrogen being such a valuable material, but unfortunately that is not possible. We need to burn hydrogen into water, waste pretty much hydrogen so that we can recover sulfur as an elemental sulfur in a solid or liquid form that is sold to a chemical industry, chemical manufacturing industry. You know that the basic material, the primary chemical that is made from sulfur for the chemical industry is hydrogen sulfide, sulfuric acid manufacturing. So you use sulfur, elemental sulfur, produced in refineries in large quantities to make sulfuric acid, which is a very important raw material or reactant in many chemical processes. So instead of mining for sulfur, as was done in the early days, now sulfur, a large fraction of sulfur, almost two-thirds of sulfur used in sulfuric acid manufacturing comes from petroleum refineries as a byproduct. Why is that? Because the crude oil that is refined in these refineries becoming more sour or higher sulfur content that should be removed because we would like cleaner fuels by environmental regulations. So dirtier crude oil means higher sulfur crude oil coming in and we need cleaner fuels because of increasingly strict environmental regulations on the sulfur content, particularly on diesel fuel, and that gives us large quantities of sulfur recovered in the supporting processes to back-to-back processes, as you will see, Klaus and Scott, to remove elemental sulfur and sell it as a byproduct from the refinery. The last process we will talk about as a supporting process is, of course, wastewater treatment. Water and steam are used in huge quantities. There is no process in petroleum refining that steam or water is not used. And of course, a refinery generates a lot of wastewater. There are different extents of contamination. There is actually steam or water that comes into direct contact with the hydrocarbons or crude oil. Those are the most heavily polluted water. They should be treated separately. One very important point to make in order to have the best water treatment process, the key is segregation of the waste streams. You don't want to mix the wastewater coming from, say, distillation with the stormwater that is also contaminated because it runs through the surface of the refinery, it may be contaminated with oil or other species. So we need to keep these stream segregators in the wastewater treatment process. And you should also make some wise decisions about water use. For example, for desalting, you don't really need to use fresh water. You can use wastewater that is contaminated with hydrocarbons but doesn't contain salt to remove salt from crude oil the very first process before the distillation.


Okay, I'm my silly thing here all the solar panels come into here and here. They don't go anywhere yet I want to split this thing in half With two different pieces and have a switch coming off one switch coming off another and Those both go to whatever kind of thing I have that goes to the power So that way I can connect half the solar panels to that switch or the other half through that switch Great. All right two switches each one can Do about 30 amps All right my copper bucket Pretty simple switch just needs one thing and another thing two pieces. That's it. Oh Wait three pieces because the pivoting part. Okay three pieces Okay, where do I put my switches All right, I think I want to cut this guy right there move this over put the switch on this side And then the other switch on this side slow speed fast speed All right slow down to stop very good. Very good. It's always important to put these these parts on the bottom So that gravity can't turn them on Now what wire do I put in there?  I'll tell me it's two separate pieces. Oh, maybe this one's long enough It might be long enough That's definitely thick enough What's that four gauge two gauge? Wow. Yeah, that's definitely fat enough The problem with this stuff is it's so stiff Like I need it to be able to move and bend like this stuff. It's much more flexible However Let's see it's triple strand Like three different wires in here And that looks like they're eight gauge Three times eight gauge wires Who is four strand I could use double and each other Oh now that could do it Four strand eight gauge and it's Nowhere near long enough All right Maybe I can find some more of that Two eight gauge wires makes roughly a five gauge wire Which is totally fine. So I'll combine two of these And then I'll have to get another another eight gauge wire to just run beside this To combine with the other one And that'll work All right, I could use that that two gauge wire over there, but it's just too stiff Like I need something that's going to be flexible that will be able to move back and forth I think this is my best choice Okay, one strand of this stuff plus the three in there Looks great plenty of length. Okay, good. I'm gonna deal with that tomorrow or the next day. I don't know Not right now. I'm going to jump in the ocean Okay, I've got my wires stripped Now I need to make connectors for them There's another thing I need to think about So the wire is going to be connected there and then it's going to come down and hang and Attach to this which is going to move so occasionally this wire is going to get yanked on So maybe I'll have it come off here Maybe I'll go right through this thing Or maybe I'll take this one off and make a stronger one something to hold the wire Real stiff so that if it gets pulled it's not pulling on this All right, doesn't seem so complicated looks about right. I want this to be stuck here Now I just got a piece of PVC and candle melted it into roughly the right shape so That should be pretty secure So I guess I should roll the lumber mill to its farthest point from here And then see how long The thing has to be to reach that far I'll just back it up as far as it goes That's the end there However At some point wanted to go a little further egg It does go a little further that way so I'll just need to Leave a bit of extra and then does the wire come through the side here or over the top I think it comes over the top Because that way when it's furthest away the wire will be you know kind of hanging high But then as it gets closer, it'll just be able to it'll droop down more Because if it's down here, it's just gonna drag on the ground a lot more. Yes over the top right Oh Okay, if I have it go over the top It'll be fine at this end But then when the the whole thing's at the other end the wire is going to want to go out the other side But then this is going to be in the way So it's going to have to go around this instead of just there so it's going to have to have this extra distance Which is silly so I think I need the wire Wait, then there's that cable there Hmm Well, maybe that's just something I Just lose a bit of space. Yeah, maybe over the top is fine And then the other option is to go way Down here in which case the wire could go all the way over there or all the way over here Hmm, well, I don't know. Maybe that's fine All right fine. I'll just have the wire go under And it'll drag on the ground sometime. Maybe uh, maybe I can have some kind of springy thing to like lift it up Yeah, that might be a good idea just to keep it off the ground Yeah, it's going to come in under here Oh, my brains are only half turned on right now Okay This is supposed to have one wire go to here and one wire to go to there And then this one is supposed to go way over here All right, let me fix that should probably connect these wires to something maybe bolt something on here That connects to the wires so these don't Accidentally touch or even move. I don't want those to move at all All right, I think everything's connected right more vibration than I prefer but it's actually not bad Um I wonder if there's something I can do to take out the vibration Oh, I don't know. Maybe I just shouldn't worry about it. It's not it's not actually that much I think most of the noise of the vibration is just because This material kind of transmits noise very easily Now I'm kind of tempted to put the blade on it See if I can find something to cut All right, I got the blade on there. Let's see


Welcome back and we are continuing our study of statistical mechanics of ideal gases. Till now we have done monatomic and diatomic and not only that we have done the statistical mechanical we derived the statistical mechanical expressions of free energy entropy and specific heat which for monatomic we did the translation that part remains invariant in the diatomic. But diatomic brings the two new ingredients one is the rotation and vibration and we have used the harmonic oscillator model of quantum mechanics to derive expression for those quantities for harmonic oscillator. And we showed that that this is one of the most respected used and time honored model applied to many systems of physics and chemistry and biology and then we did the rotation using the rigid rotator we worked out again the statistical mechanics. Now the most many of the systems that we are interested in like water ammonia alcohols they are all polyatomic molecules and polyatomic molecules have characteristics which are quite different from that of diatomic. The reason is that the polyatomic will have now in addition to translational degrees of freedom in addition to translational degrees of freedom at in rotational degrees of freedom it has vibration which is many more now as we all know that vibration number of vibrational degrees of freedom is more in case of linear because their rotation is only two but for non-linear molecules where you have three rotation we have three and minus six the vibrational degrees of freedom and this is what actually gives rise to when the large molecules like polymers form or when they form they are sitting together in a crystalline forming a solid amorphous then we lose the translational degrees of freedom that they have and that get transferred to vibration degrees of freedom and that showed up shows up as a normal mode which has played so important role in the specific age and thermodynamic properties of low temperature solids not just crystals but also amorphous materials and these are low temperature liquids they are very very important quantities. So but however the polyatomic molecules have many other peculiarities of their own that we are going to discuss today and they want to do a how to do statistical mechanics of polyatomic molecules so that a student knows how to start talking of entropy and free energy and specific heat the molecular component of the polyatomic molecule and that statistical mechanism gives you and we already have it but so we will have a slightly more generalized form of what we did in diatomic and so it will be it will be not too demanding a session we did do in a small way the polyatomic earlier but we are going to do a little bit better now and in certain sense also it is a review of many of the things that we are going to do okay and we wrote down before we are neglecting the electronic degrees of freedom because electronic energy level gap is much larger typically electronic energy levels are of the order of say 10,000 centimeter inverse 7,000 centimeter inverse which is huge so they do not enter at the room temperature the ambient conditions electronic degrees of freedom it does not show up in the thermodynamics it does show up in the spectroscopy when you are giving external source of energy and resonance condition and exciting but in the thermodynamic properties it is a ground state of electronic degrees of freedom that that is all that you need to worry about and we can take that energy as a zero so that just it does not change its temperature does not change its pressure problem we do not need to talk about it. So then I can write the partition function as a product of three as we already discussed that it is translation these are molecular partition function so this is a molecular partition function and these okay the molecular degrees of freedom the molecular partition function q small q is my notation for and capital Q is my notation for the partition function of n particle system so then this q translation q rotation and q vibration now translation is the center of mass so we do that then if I have a nonlinear molecular three rotational degrees of freedom I call it q dot 1 q dot 2 q dot 3 and then I have the all the other degrees of freedom that is given here and that is of course not just three if there are three vibrational degrees of freedom then it is 3 but otherwise that can be many more degrees of freedom that would be showing here so and that is shown here so since they are all these vibrations are a independent of each other the normal modes then q vibration is a product of all the vibrational degrees of freedom which is written here that I have a new stands for vibration in the notation and j is the different normal modes so then my total vibrational partition function is product of e to the power minus theta j by 2t and by t because the remember theta and this is the alpha is given here and theta uj is the vibrational temperature and this one is the one that comes from 0 point energy I to remind you and this is the one that comes from the detailed sum of this power series with x a 1 plus x plus x square and that becomes 1 for x less than 1 because 1 over 1 minus x so this is the one we derived it derived in the in the last or the one before last class so now if we know this so then we can set up the partition function now so vibrational part is fairly simple vibrational part is fairly simple because we have this thing and you give me the frequencies and give me the that gives me the vibrational temperature and I can I can give you the partition function so now we will concentrate on the the rotational part rotational partition function has is very important in polyatomic molecules and because there is a you know this kind of can be jittery and all the kind of motions that many times you face are basically some kind of restricted rotation now rotation has fairly different cases we need to consider one case where all the momentum inertia are the same because there are three direction in an all linear molecules and you can have three principal axes and you have three momentum inertia now if this completely spherical we call spherical top molecule like methane then we have no problem we have all the momentum inertia are the same which is like I a I b equal to I c the spherical top the degeneracy of the rotation as it becomes 2j plus 1 square if they can equal principal momentum inertia then all this and we can then write these 2j plus 1 the degeneracy of the rotational energy levels the equal principal momentum inertia is then you do instead of this product we will have 2j plus 1 square and then we get this expression for the rotational partition function and then we take the following limit at high temperature when temperature becomes very high then and a momentum inertia also not to small then the the ones that will be involved at very large j large quantum numbers will be involved and large quantum numbers then I can I can approximate j plus 1 by j that is a very neat neat approximation and then my rotational partition function becomes this become 4j square then it becomes like then it is a beautiful thing so in the high temperature limit I can do this integration now it is long that the difficulty I had but remember even in the diatomic case we could evaluate we could evaluate the large high temperature limit here also then the high temperature in in in the polyatomic case the high temperature limit can be worked out and again we get a very neat expression of the rotational partition function so continuing we now do symmetric molecules now symmetric top molecules are the ones who which are like symmetric top which are two momentum inertia are the same and third one is different it can be prolet in the prolet if it is a prolet then then in this v and c are the same momentum inertia and this a is different so momentum inertia ia is let is then ib equal to ic that is prolet and it can be oblate in the oblate case then it is these things so this direction c is different from in the in the spherical direction is a and b so prolet and oblate are two different things and in that in that case we can calculate the partition function by using the method similar to this one that remember that if you go to rotational case in the diatomic case the partition function is 8 pi square i by kbd 3 by 2 x square then the same thing happens here so the quantity is that two of them comes with 8 pi square ia kbd by a square half and half so when a equal to b when a equal to b then this half and half becomes just one and then you have this c half okay so whatever I do either prolet or oblate depending on a and b like for example in the case of prolet it would be a here and then okay b here and a here in the case of oblate the other way around a here and c here just just the same thing of course the values can be very different so but then one comes the most general case with the asymmetric top molecule in asymmetric top molecule all the principle moments of inertia and this is the general case by the case of water molecule case of methane they are all asymmetric top molecules where all the moment of inertia are different and this analytical expression might be levels cannot be obtained by solving equation that is the real unfortunate part so in the previous case part the this case these thing comes from solving the sorting equation the degeneracy factor of a spherical top molecules that it is 2j plus 1 plus whole square therefore a polyatomic molecule this is comes from sorting equation however this k in the case of completely asymmetric molecule we cannot do we cannot solve the sorting equation and as a result we cannot get those energy levels so sonic equation can be cannot be solved analytically so for the diatomic we get analytically for for symmetric top the spherical top we get in analytically with the different degeneracy now for the polyadenoblate we again get polyadenoblate when they are they they they they decompose separately and we can get the energy levels again and we can solve for the at least high temperature limit the partition function but in the case of fully asymmetric molecule where moment of inertia ABC are different it cannot be we do not have any close form analytical expression for the energy levels and that was the problem so in that case the sonic equation has to be solved numerically to obtain the energy levels this is very very difficult and these are laborious process these are laborious process but the we can we can obtain to this the classical limit the high temperature limit that the high temperature as I said the quantum goes over to classical partition function in the in the high temperature that means I can start partition function from classical Hamiltonian I can do from quantum Hamiltonian then I can show that high temperature the quantum goes over to classical it is very nice and has to be because there is nothing you know surprise there at all but in this case where you cannot do anything in the for the for the quantum case because energy levels are not known we can do anything other than numerically that is actually done many many cases numerically one solves and gets a but we we can make progress with the classical Hamiltonian which can be done and classical Hamiltonian of course can be just integrated I write down the moment of inertia I have ABC and write down the there is no there is no potential energy still it is just the rotating and it has the rotational kinetic energy and rotational kinetic energy I know how to do the rotational kinetic energy the rotational angular momentum divided by 2 I and then I can integrate that and that we will we know that that gives this kind of form so now I have one for a one for b and one for c so I have three and part total rotational partition function in product of these three which is just the one we got in classical from classical statistical mechanics or the high temperature limit of the quantum diatomic case with one moment of inertia but here also when they are written in terms of momentum inertia they are already decomposed and then we can get that and then we can write the rotational partition function I can combine these things and define a theta a theta b theta c in terms by using all these quantities because that quantity then becomes one over theta b sorry one over theta a and that becomes one over theta b and this becomes one over theta c then my partition function becomes this quantity root over pi by sigma t cube theta there is a way very nice and need and very elegant expression and remember the half is preserved now each comes with a half and that half shows up here so this is the rotational partition function that complete rotational partition function of a polyatomic molecule. So now we do we have this so we go back and we have the we have the we go back and we have this total partition function and now we want to do certain thermodynamics with this expression and what are the kind of values that you get okay. So let us now consider some specific cases now the temperature the rotational temperature and vibrational temperature gives you a measure is a very important thing they give you a measure of the quantumness of the system and the importance of that particular mode in my thermodynamic properties for example in case of water I have three vibrations what are the three vibrations one is symmetric stretching one is asymmetric stretching other is bending the three vibrations for water now look at them we already know one is 3650 centimeter inverse symmetric stretching a little bit higher is symmetric stretching that is 3700 centimeter inverse bending is half of nearly half of that that is 1885 centimeter inverse very nicely placed those three and that plays a very important role in vibrational relaxation there is some of the outstanding discoveries that made in recent times okay now if we do that then look at these in case of water so this is asymmetric stretching this is symmetric stretching this is the bending all right now if it is so then I can easily see that in thermodynamic properties my if temperature it will be relevant at 5000 Kelvin no so at room temperature I do not need to worry I do not need to worry at all for water but look at rotation rotational temperature are really very low the three momentum inertia of asymmetric that water molecules with three axis of rotation they come so it is temperature that means they are they are almost classical and I they they influence the statistical that influence the thermodynamics so I need to take into rotational degrees of freedom in understanding thermodynamics and these are the very interesting story so for some time quite some time people are trying to calculate the entropy of water this is actually big game now of last some 15-20 years what is the entropy of water because the entropy of water as I said plays a very important role in many many chemical reactions and what I give you an example when a DNA drug goes into a drug goes into DNA then of course the drug loses the entropy but the system gains entropy the way system gains entropy the water molecules which were inside where in biving where inside the inside the major and minor groups they are displaced so when they are in minor group they did not have any entropy there is some extra enthalpy but they are no entropy so when they go out they gain lot of entropy so we kind of take into account away that 10 molecules that are yet in this space that 10 molecules going from minor group of DNA to water so what is the entropy for water molecule if I know then 10 times that is the entropy gain in the process and then I can use substituted equation or something to get the but substituted equation still in a liquid water is not a great approximation but in that that they get you started very very interesting now when all these calculations were done in initially people are not getting very good agreement of the entropy of water in the and entropy of water can be obtained also experimentally in a laborious process by starting from all the way from zero kelvin ice then going into make it melt going to liquid then you know we can calculate at take the latent heat of fusion into and we know the entropy of water experimentally that was not working that well then we realized that we did not take into account the vibration and rotational entropy contribution but as I show you vibration is not important but rotation important translation is of course important so it turns out the rotational in contribution to entropy of water is about 30 percent is a huge contribution that comes from a rotation it is something like that one in the entropy unit rotational contribution is about 5 or 5.2 and the translation contribution is 17 so if total entropy is 22 you already had a table saying 17 the translation comes and then this this this another five comes from and you know to calculate that entropy I have to calculate I have to use I use this expression this expression I use to calculate the rotational partition function I get the free energy a equal to minus cavity l and q and I take the derivative of that and get the entropy that entropy now is an is extremely important contribution for water rotational entropy contribution at room temperature is 30 percent of the translation contribution this is a really very important that we missed you know very recently that we missed this thing this is just about I think 10 years old now another system interest is ammonia in ammonia has again this ammonia has four vibrations it is stretching anti symmetry stretching and and and bending mode now those are vibrational temperature the theta 5 that we define in terms of the frequency and that is pretty large so one is 4800 that is very large a vibration this another vibration these two are some kind of bending modes I do not remember fully the mode but they are they are certainly not one stretching modes but even then these are pretty high temperature the room temperature remember it will be e to the power minus the contribution comes as e to the power minus theta by t that would be theta vibration by t and since theta vibration is so large temperature at at at at 300 Kelvin even this guy is e to the power minus 4 and yeah 4 point something these are of course much larger so this contribution is minimum however the same e to the power minus theta rotation by t all in Kelvin look at that this theta is small so all these things play very very important role so all these three modes play very important role in the entropy or the thermodynamic properties of ammonia similar things you find in sulphur dioxide nitrous oxide methane everywhere you see the vibration temperature is very high so when it comes e to the power minus theta vibration by t the vibrational degrees of freedom do not contribute significantly at ambient conditions to the thermodynamic properties so molecular thermal molecular partition function and molecular thermodynamics the vibration is a silent thing we do not see it we find huge contribution of translation but then a significant 20 to 30 35 percent contribution comes from rotation so rotational degrees of freedom cannot be ignored in find what you are doing and this is a very very important thing because see most of the books and most of the studies that we hear everywhere that people are doing they they they as if the world begins at the ends with monatomic molecules maybe a little bit of diatomic like take take the phase transition theories and all the things that we will be doing something we we we start with sphere spherical molecules you know and we end with spherical molecules like about studies of glass transition theory do theory of liquids that we do they are all models are things who called in adsorbed models and others but they are all spheres but this is something so when we did statistical mechanics in 1970s and 80s we learned towards the end of 70s and 80s when I was doing PhD and post off we really never bothered about you know if the popular text books of statistical mechanics they do not have much of polyative molecules so our our emphasis and the book that I have written the statistical mechanics books for chemistry and material science that is why we have a a very big discussion of polyatomic molecules and a lot of emphasis given on polyatomic molecules because these days we are interested in these kinds of systems okay. So let us continue then then entropy of a polyatomic molecule is a just a wonderful thing as I just discussed to you so this is the thing the translational part so entropy since put a partition function is q translation q row vibration and q rotation and then free energy is minus kbtl and q so these that they decompose free energy become some of the free energy and entropy becomes some of the entropy this is trivial but sometimes it is good to spread out the trivial thing because to help the thinking that is then this is our circuit tetrodiquation this is the circuit tetrodiquation and then this is the rotational now I have arranged it such that most important thing in translation which water and ammonia has about 65 to 70 percent of the total entropy then the rotation which is classical limit but classical limit works out reasonably well as I showed you in these things fortunately for us this theta vibration is small so we are okay because the room temperature is much larger than this so we can rely doing classical mechanics this is a lucky break in quantum no way it is too much it is too quantum but this is nearly classical it is very very very interesting how lucky one can get some time so like for translation you get away by the classical mechanics for rotation for translation you get away rotation you also get away by doing as I showed you for many of the molecules vibration we are not that lucky but vibration with the harmonic is a good approximation so this is translation these rotation and these are vibrational contributions to the total entropy and as I said this is actually negligible so these two does the job perfectly for us so now where I have given you a table actually this I have preempted little bit I told you I already showed the table 70 and 5 which is I was talking from memory but there it is that water molecular weight and every detail is given and these are the three moment of inertia I have given you what are these are the things you do not get in the physics textbooks and or even earlier versions of stat mech but now these are so important in the present in search and present the calculations that polyatomic study of statistical mechanics of polyatomic molecule is important thing that is what I am discussing it though I discussed this a little bit before I am discussing it in more detail and as I tell there is no damage is done by doing it these beautiful things more than once okay so look at that to in water has this nice thing is the two of the moment of inertia very close to each other and these are these two a and b 1.09 1.91 and this is quite different now this what I was saying 17.41 is a translational part in the entropy unit in the KB and this is the one that rotation 5.45 but look at vibration contribution is negligible when you add up all these things you get this is the entropy of water beautiful very very nice now the other thing as a ammonia ammonia there are these things that two things that nearly degenerate and then this one is larger moment of inertia now a very similar story unfolds for ammonia translation and rotation now rotational contribution little bit larger that you could guess because go back you could guess that it will be larger because look at the rotational temperature rotational temperature of ammonia is lower than that observed so as soon as rotor temperature become lower its contribution becomes more to the partition function and to free energy and to entropy and right that is the one that happens so 5.45.91 this is slightly less but then at the end of the day we have these value of the entropy and as I said there are very important things in property to get the ideal entropy there are many expressions of entropy and for example connection between diffusion entropy there is a property called Desmond Rosenfeld scaling which needs the ideal entropy ideal gas entropy and what uses the value of ideal gas entropy of water molecules to predict the diffusion constant in liquid which certain other other terms involving but this plays a very very important role in in the property of liquid okay so this area I summarized it here that the this is straight from the book statistical mechanics book the Statemac book by CRC praise from that it is taken that a transfer entropy contributes in the most but also rotational contribution is this is my favorite I did not know myself about five six years ago the rotational contribution is 30% because we also grew up like doing as if the everything is land zones as if there is everything can be modeled that spheres but then you miss out all these things molecule vibration entropy is only only considers intermolecular model are not very important so by the contribution lies from vibration is negligible so this is very encouraged to carry out numerical calculations of polyunet molecules like chloroform this is a this is a homework that will set up to make you do something like methanol and you can calculate them by doing the homework so here ends the statistical mechanics of ideal gases we I just summarized what you do in one minute that we have done now in great detail monotomic gas which is spheres non-interacting spheres then with the diatomic like nitrogen oxygen they are rotating and they have a vibrational degrees of freedom vibrational degrees of freedom has beautifully comes with these harmonic oscillator and the flooding gets the solution and however in thermodynamics those vibrational degrees of freedom do not play in old but translation rotation place then we went polyatomic molecules and we did statistical mechanics of polyatomic molecules the very important case of water very important case of ammonium or other sulfur dioxide and all other important molecules that we need to do in everyday life and in a real problems like you know and that then at the end of this part so top here we will take a break and we will go over to the next class.


What does success mean to you? This question will present a lot of different answers from everyone, because we all have different goals and ambitions. Hence, it is whatever we want and trying to reach that determines how to define success. To some people, it is when we get a particular sum of money in their account that they believe they are successful. For some, it is when they get married and raise their own family that they accept that they are truly successful. Here's the thing, maybe we all want different things in life, but it doesn't change what success is to everyone. Success has just one definition that should always count, no matter what our goals and ambitions are. When our lives, work, career or whatever else we want goes by this definition, then we can say that we are truly successful. So, in this video, I'll share with you the only definition of success that matters. If you're new here, consider subscribing so you won't miss other exciting videos like this. 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But basing your success on one or two achievements is a frustrating way to live because as humans, we will always want more and are never easily satisfied. If we live that way, we'll quickly become disappointed and tempted to give up whenever we don't achieve any of our goals. Anyway, we now understand what success isn't. So what then is it? What one definition of success matters most? Here we go. How happy are you? What do you do that makes you happy?  Abraham Lincoln, an American statesman and lawyer who served as the 16th president of the United States, once said, In the end, it's not the years in your life that count, it's the life in your years. You want to make more money, build a successful business and career. Whatever it is, it is what makes you happy that counts. Think of what motivates you to keep moving and putting in so much. That one thing that you desire to be successful, it could be spending time with your family and loved ones. What motivates you? What do you want to achieve for yourself and your family? What do you value most spiritually, emotionally and materially? That's what will make you happy and if you aren't doing it, you won't be satisfied no matter how much wealth you have or not. Here's the thing, happiness isn't found in what you have or don't have. Although it is tempting to think that the reason why you are not happy is that you don't have something that you earnestly desire, but the truth is that you haven't learned to create happiness independently of what you have or don't. Thomas Jefferson, American Statement Diplomats Lawyer, Architect, Philosopher and Founding Father who served as the third president of the United States said, Our greatest happiness does not depend on the condition of life in which chance has placed us, but is always the result of good conscience, good health, occupation and freedom in all just pursuits. Again, according to Lou Holtz, a former American football player, coach and analyst, life is 10% what happens to you and 90% how you respond to it. It means that it's not the things that happen to you that make you happy. It's how you choose to react to them and when you understand where your happiness truly lies, you'll be surprised how successful you'll become because you won't waste your time or effort chasing the wrong things. Things that will never make you truly happy except that they may bring you temporary satisfaction and that's it. Let me tell you a secret about finding what makes you truly happy and successful in return.  Also, according to Rosa Parks, an American activist in the civil rights movement best known for her pivotal role in the Montgomery bus boycott, each person must live their life as a model for others.  Think of people whose legacies remain till date. Why do you think they became so important to our present day life even though they are no more? It's simple. They live their lives for others. Think of Abraham Lincoln, Nelson Mandela, Mother Teresa, and others who are not necessarily activists but whose lives and innovations added value to humanity such as Thomas Edison, Steve Jobs, Walt Disney, etc. They all wanted to do something beneficial for people. To them, life was beyond their own lives alone. And this is where true happiness lies. For instance, you could tell a teacher who is complaining that they are not well paid to change their job and they would respond with something like this, oh no, I could never do that. I could never sit at a desk for 40 hours a week. I love what I do and I just don't like the pay. In the end, what they do positively influences lives, matters more to them than money and that's what success truly means. So, the definition of success that matters is how happy you are and how valuable you are to others. Thank you very much for watching our videos. If you like this video, watch more videos on our channel and subscribe. We love you.


ಯಽರ್ಳರರಿ ಠೀಂತಿದದ ತಿರಿಲಿಲಿ ಙಬಱುಲಯಾ್ದುದ್ದಮ್ ಭಕಿಮಾರೆ ಮುನಿಣದಿನ್ನನುಗಳಿದುಗಳರಿನುಗಸ್ ನರ್ಲಿಕಿಕುದ ನಡೆಯಾರೆನಿನ್ ವುನಿನೆಗಳಿನಿಮ್ನಿನಿನುಡಿವ� ◩ . ◩ I'd like to take you through a journey of one 45-year-old gentleman who was basically a software engineer who presented us in the year of 2017 with a small pain and a bit of bulge in the upper- ಕೆ್ಟ್ಟಾಲೆಕೂ ಕಾತ್ತಿಸುಗಿಲ್ ಪಿಜ್ಂದೆ ಕಾಚರ್ಂ ಪೆಳರದನದೆ ಚಾರೆಂದಲ್ ಢೆಲಾರಿ ಹೊಥದೆ ಮಲ್ಟಾರ್ಧ ದಾಸ್ರ್ಗಿರ್ರೆ ಆಲ್ಣರ್ರಾರ್ರಯೆ ಹೊತ್ರಾಾಲ್ಲಿಸ್� up猎 ಕಾರ್ರೋರಗಳರ the anterior chest wall along with a part of the three ribs in a way that there was no spillage of the tumor and also preserving the heart and the lung in the vital organs across and following this the plastic surgery team reconstructed with a muzzle flap and we also put a couple of plate and screws to allow it to stabilize temporarily which was removed a year and a half later. Our patient had a rare problem called condosarcoma of the sternum that's the breast bone which was quite big so in total because of her multidisciplinary involvement we could remove it and give me a result which was as good as it could be it's been more than six years since Mr. Dewey and I went to treatment he's cured now he was able to carry out all his activities and he went back to work within just two and a half months to three months of surgery and this approach encompasses or showcases the way we take care of our patients with the help of a multidisciplinary team. Multidisciplinary approach certainly gives much more value to the patients and that is where we as Manipal being here for more than close to half a century now fall into place there are departments everything we can imagine which gives the care which probably they would get from the best of the places


What's going on guys welcome back to the channel critical overload here since my Halloween ends in this video here today now What you see here on your screen is a message that I had gotten the day after the 4th of July for one of my Sources that I trust who share information with me about certain upcoming projects They should decided to share information with me about Halloween ends saying that ends is dealing with a new kid Who killed someone and hadn't felt treats him like Michael, but we don't know if he's evil or not So it's more about the nature of evil than anything else Myers does come back But not until later in the film. Now, here's the thing This was something again that was told to me the day after the 4th And then of course, I just waited to see if it ended up being true And it was true in the sense that the kid's name is actually Corey Cunningham He is played by an actor named Rohan Campbell and Going off of the synopsis that reads four years after her last encounter with the mass killer Michael Myers Lori Stolt is living with her granddaughter and trying to finish her memoir Myers hasn't been seen since and Lori finally decides to liberate herself from rage and fear and embrace life However, when a young man stands accused of murdering a boy that he was babysitting It ignites a cascade of violence and terror that forces Lori to confront the evil she can't control now when considering That synopsis mixed with some of the wording here and some of the shots shown in the teaser that's been released where we see Michael Myers at One point. He has a ring on his finger It doesn't really match knowing that Michael isn't supposed to have certain fingers And then we see Michael again later on battling Lori where the hand seems to be more accurate in certain limbs Are not there so again going off some of the wording It says when a young man stands accused of murdering a boy, he was babysitting This young man. No doubt is gonna be Corey Cunningham It's it's like, okay. Something's going on here. I would guess where Corey Cunningham I'm gonna just speculate real quick might have some type of obsession with True crime in some capacity He could be somebody who's obsessed with a lot of these different killers that exist and Michael Myers is now his latest obsession. Let's say that's the route we take in this upcoming movie He could be someone who isn't even Haddonfield resident he just recently moved to Haddonfield and There's something about Michael Myers that he has become recently obsessed with just like how he might have been obsessed with another killer in the past like a Ted Bundy, let's say or something something else like a John Wayne Gacy or you know something like that which is actually stuff that was touched on a little bit in Halloween resurrection But let's just apply that to a different character now in this timeline Someone who's obsessed and that obsession probably goes a little bit too far There is a shot of Corey in the teaser if I'm recalling correctly where it looks like Michael grabs the boy and It's choking them briefly in the sewers. So some type of encounter goes on so maybe he went looking for Michael and This is something he was doing in secret I would say because again the assumptions that he's gonna be dating Allison in this upcoming movie doing this in secret because he knows about the trauma Michael calls Allison So he's doing this in secret He ends up stumbling across Michael has a brief encounter with him and Escapes with his life now. He could have also escaped with something else Michael Myers mask So here's what could also go down in the opening. We see that somebody is Stalking a house. We hear heavy breathing. I've seen some people already address that does not sound like Michael Myers breathing patterns That we're accustomed to and then again with the shot of what you see on your screen Transitioning into Lori standing in the door frame with a with a gun clearly showing us something completely different as far as what's in the background of The rooms prior to that I'm thinking okay This is the boy that was being babysat and what happened with Corey is that maybe he decided to you know play a prank the prank goes horribly wrong and That's why he ends up being Being accused of this heinous crime. He didn't do anything, but his obsession Allowed him to of course do something do something that he thought of course would be ultimately harmless Just put on the mask of Michael Myers and scare the boy or whoever it is He's pranking or every it is he's babysitting This leads to their demise and that doesn't end up well for him because he was the only one in the house with The child he didn't really do anything, but the whole town of Hatterfield is just blaming him blaming him blaming him left and right Nothing really comes of this because there's no real evidence of it Let's say that he did anything to the child and then all these years later Allison is stood by him He is talking to her about some of the obsessions he had revealing his obsession with Michael Myers to Allison and The whole town just hates this kid He's despised in the town for what he's done because they they're tired of this They want to be rid of anything that might resemble Michael Myers and what he did to them 40 years ago and four years ago now and all this terror He's caused them in the community and how they respond to evil Is a little bit toxic in a way I guess you could say given that Corey in it of himself He didn't do anything in the sense that he didn't even kill this boy So what ends up happening is Corey could be someone who decides you know what if they want Me to be the essence of evil. I will give them the essence of evil He decides to become a Michael Myers copycat killer He decides to go out of there go out of his way and attack certain people who might have been a little bit more nastier to him than others in the community of Hatterfield and this ultimately leads to a Confrontation that goes on between himself and Laurie strolled but Michael Myers himself also returns during all of this as well Which could lead us to a scenario Where Michael kills Corey? Who is at this point I would say been pushed over the edge mentally and this obsession He had with true crime would also factor into that and his obsession with with serial killers and other things like again He could be someone who moved into Hatterfield We don't know much about Corey cunning him He could be a kid who moved in the Hatterfield and always had an obsession with killers and true crime and Michael Myers Was his latest obsession so this move in was perfect for him And this led him down a very dark path given how the town of Hatterfield responded to him after an unfortunate accident Results it in the death of a kid. He was babysitting when he was pranking them dressed as Michael Myers Let's just say that's what happened. He didn't do anything But then the whole town doesn't like him he decides you know what I'm gonna give them what they want They want they want me to be evil. They won't let me be good So I'll just be evil goes out of his way dawns the mask He gets to live out this obsession he has with these killers and even in body and maybe in his own mind get to see what it felt like for them and this ultimately of course would lead to Michael Myers ultimately returning to Hatterfield Corey gets taken out and Lori Stotter Michael Myers have their final battle now a lot of that in between might sound like again something and I'm already can admit I don't even necessarily want to see them do something like this I'm just thinking about a narrative. They could give us with Corey But let me know what you guys think about this down the comment section below Do you think this is something they could do? Is it something you actually want to see them do if you haven't already subscribed turn on post application there miss a video in the description I have links to all my social media accounts on Facebook Twitter and Instagram You can message me there of course to let me know as any movies news or reviews Let me to cover in the future and with all that in mind guys. I will see you in the next video