Hello, I'm Amis the Steve Rose as we do each and every Monday at 20 past the hour and don't forget folks Steve has an outstanding show here every trading day one to two eastern standard time also great newsletter mastering probability Now it's very easy to get Steve's newsletter folks in a great time to get it because we have a traders market There's no doubt about that man come over to our website at TFN You go around the newsletters You're gonna see mastering probability on the right-hand side. You just hit subscribe You can get mastering probability for one month for hundred and forty nine dollars You get it for six months for 695 which is a savings of 199 dollars and you get it for a year folks You're 1195 which is a savings of 593 dollars of 33 percent Steve Rhodes, what's going on? Well, just shifting them my sports gears from football though We've got a good game coming up next weekend. Let's hope to do things like hockey and in the Olympics I don't if you've watched watched any of it I've I've I've been watching a little bit in the evenings like about 10 o'clock in Yes, if I'm up in and what I saw the first couple of days was the snowboarding women snowboarding I saw that. Is that amazing? It is amazing man Can you imagine going down those hills and and doing what they do? No, and you know, I snowboarded But I never made it by the bunny slope When you're snowboarding on a bunny slope, let me tell you you're going fast. Yeah, I have no idea how they do that Yeah, yeah just really hurts because you follow so many times. Yeah It's a man and some of these women when they've when they have fallen, you know, they've got such flexibility Yeah, they're able to pop back up. It's amazing. I know man. Yeah, I mean you're thinking they'd be broken bones all over the place But they've got such flexibility. So I've really enjoyed watching that. How about the you're talking about that How about the the losers? Yes, right? That's another amazing a sport. Yeah, there's a mind blow You know, you know what the cool thing is we haven't made for the next two weeks When it's just so you know folks what you can listen to a six o'clock in the morning six o'clock at night It doesn't matter. It's on two stations though Yeah, just go down further and this it's almost on 24 hours a day, which is really dynamite So yeah, it is like when we're watching to lose my wife said to me. She said So what do you think those people are thinking about I said what I'd be thinking about is staying on that board Not and that's flipping over and sure enough about 30 seconds later One of the guys lost it was flying into and that's I think that's actually more dangerous on the lose track Flipping over because there's no way to stop. Oh for sure. I didn't see that. That's yeah. Yeah, luckily the guy was okay But you know that I don't I don't think you get me on a lose. No, or don't it or on a Did it that would have been great. I would have stayed on it all day, but guess what that you know We want to live for a while here, man Yes, we do. Yes, we do. So let's get to the markets out here We always typically start just the refresher. Hey, where we at in the seasonal pattern out here So we know that the Dow typically tops folks in January early January and then bottoms at the end of January and this year Here we've got the Dow topping on January 5th and so far the bottom is on January 24th So the seasonal pattern is oh, it's not even be showing your hold on a minute here. Give me a moment. Sorry about that That's all right. I'm showing the wrong screen Do that on occasion but in any event, so I'll just go back real quickly folks Here's a seasonal pattern. Yeah, there we go And then you've got the January 5th top the January 24th bottom out there now Well, we really start taking a look at so what I want to do here Something different than what we've done in the past is just really take a look at some of this or the sectors inside the S&P 500 and some of the top-weighted instruments that make up the S&P the Nasdaq in the Dow and what I'm doing here is giving a bigger picture So these are annual charts yearly charts that we're taking a look at and this is the one key thing that Everybody that's listening to us. You don't have to be a technician You just have to have access to a charting application And what I can assure you is that when you're taking a look at an instrument if price is trading above the prior year's high So 2021 is high Yes, you're in a bullish or a breakout mode and if you're not trading above that you've got something else that's going on That's especially important for us right now. So here you've got the S&P in the upper left hand corner We can see that it's trading below last year's high. So too is the XLK. So too is the health care sector So too is the consumer discretionary sector now the XLF This is interesting if the XLF can close above 4086. It's going to be in breakout mode So it's got some possibility and potential But if we go down one level lower and you were talking about the energy sector earlier with your pride in your primary segment here That is in full-out breakout mode now people didn't necessarily need me to tell them that But it is good to have the visual to really see what's going on So the the two hot sectors right now inside the S&P as the energy sector and potentially the financial sector Otherwise everything else is trading below 2021 side and says be careful be cautious out there That's good to know man. I remember seeing this last year. I remember the same deal, which is so cool Go ahead Steve. That's this is cool man. Yeah, it isn't it because it's something easy for everybody That's listening to us to follow along You know we start talking a to b equal CD oscillator and changeline all these things and it can confuse people But this one simple now here Tom This is a set of charts looking at the futures contracts out here So in the upper left-hand side, we've got the US dollar index if it starts trading above 96 94 It's going to be in breakout mode and I'm going to go all the way over on the right-hand side in the center here You've got the tenured treasury note now You already know this but now that people can see this it's trading below last year's low Folks that's very bearish as long as that condition remains out there. That is a bearish Pattern if we look at go down to the lower line out here, we'll see that rice is breaking out So we've got rice that's going up in price. We've got soybeans that's getting ready to take out this 15 86 40 level That's going to be in full-out breakout mode You've got light sweet crude in the upper left out here 85 38 as long as price remains above that It's both now what's helpful about this for folks is to try to take a look at those things that are bullish Those of you that want long trades energy trades things of that sort You now know where to focus your time in the futures market if you're looking at commodities rice and soybeans are really important to Be watching and if you're long on a tenured treasury Right now you you really need to have a good bottom pop Tom because you're trading below last year's low That is not a good thing if we shift over here to the top holdings inside the NDX 100 You got Apple leading the way Microsoft but you can see each of these are trading below last year's high So they all suggest to be very careful out here now Facebook Facebook's got some real problems because it's trading below 244 61 so this could be in Facebook Tom This is the first year since it's been introduced from since it's IPO This is the first year price has even been able to get below the prior year's low Wow, so this is telling us there's some really significant issues going on inside of Facebook If we look at the Dow in the top 10 hole or the top holdings out here That shows no breakouts, but it does show that Honeywell, which is the three four eight the 11th weighted Instrument inside of the Dow that is trading below last year's low 195 so anybody that has it as long-term holding you should really take you should really watch that 1955 level and then finally the S&P 500 here's the top 12 instruments inside this was interesting I didn't realize this till I put together this chart The only stock that's breaking out is Berkshire Hathaway Wow, which typically follows the S&P 500, but it does not appear to be following the S&P 500 this year So the weighted underline instruments They all suggest caution and so too do the yearly charts and you and I've talked about this many of the yearly charts Have these TD nine count tops and that's where we can definitely see price pull back in so far That's what we have seen unfold Shorter term what I want people to realize is that we should see a bounce The reason we should see a bounce is on a weekly basis the Russell 2000 That's a very right-hand corner panel Yeah, formed at Gartley buy pattern and this little oscillator and change line change colors So we should see this move up to the 2140 level. How are we gonna know if we're gonna see this rally folks? Well, I'll just take a look at them just moving here to the futures contract. There's these descending trend lines Tom, I think those are the real targets whether we get an A to B equal seeding to the upside Well, it has to take out those swing points But right now the Russell 2000 is the first one to test in trend lines So everybody's deep an eye on the Russell and foot what an awesome updates deep and folks It's really easy to get his newsletter come over to our website the TF and in get that master in probability It's gonna help you tremendously man. It just helped me tremendously. Have a great one. Have a safe one Steve. Thanks you too


What is the difference between the self and internal objects, and what are self-states? How are they formed? How do they function? Who calls them forth? Who coordinates their appearance and disappearance, the process of switching? I have dealt with the first question in my previous videos. The self is an internal object, but it's a special internal object. It's a privileged internal object. It's the only internal object that communicates regularly and multiply with all the other internal objects. Now the other internal objects in the narcissist's mind, and the borderline's mind, the other internal objects can communicate among themselves and sometimes do. But the flow of communication is limited and intermittent. The self, on the other hand, communicates with all the internal objects all the time. The self is like an observer, or a teacher in a classroom, or a parent in a family with many children. So the self introduces order, structure, regularity and predictability into the internal environment. The self is the pivot, the self is the core, the self is the axis, and the self has many attributes, characteristics, which are essentially divine in a way. The locus of grandiosity is in the self, the locus of healthy narcissism is in the self, etc. So the self is one of the internal objects, but the most senior. And in charge, the self is the authority, the internal authority within this family system, within this multiplicity of entities. Now some of the entities are introjects, they are inner representations of meaningful, significant others, parents, sometimes intimate partners, peers, etc., etc. Some of the internal objects are constructs. Some of the internal objects are actually not objects at all, but processes which are so common and so repeated, that they are routine, they become embedded, they become kind of structural. So this whole gamut of internal objects is the inner landscape. Now the narcissist has many, many internal objects, but he doesn't have a self. He doesn't have an ego, he doesn't have the coordinator. He has many internal objects which communicate among themselves, usually conflict among themselves. They're in a conflictive state. There's a lot of aggression there. There's a lot of dissonance. There's a lot of ill it is. There are many compensatory mechanisms. There's an attempt to somehow regulate the inner environment by importing, by introducing feedback from other people. This is known as narcissistic supply, but it's a mess. The narcissist's personality, the borderline's personality, they are disorganized. They are chaotic and they are chaotic precisely because the ego is fragmented. There is no core identity and this is known as identity disturbance. So if the narcissist and the borderline and the schizoid and the paranoid and the codependent and so on, if they don't have an integrated self or in Jung's language, if they don't have a constellated self, if the process of introversion and investment of narcissism in structures, in internal structures, in a healthy way, if this process was interrupted, disrupted, didn't work well in early childhood and consequently the adult has no integrated self, no unitary self. Then what are self-states? How can one have self-states without self? It seems contradictory. My name is Sam Bakning. I'm the author of Malignant Self-Lover, Narcissism Revisited and a professor of psychology and I'm here to answer this and only this particular question. I'm going to shock you with a short lecture rather than a lecture which lasts a whole lifetime. So, do you remember in my, or you don't remember, in my lecture, previous lecture released today about how the making of a narcissist, it's a cautionary tale. Even good parents or parents who consider themselves good can create a narcissist. So, you'd better listen to that video if you're parents and learn what not to do. Anyhow, in my previous lecture, I described the formative years between zero and two. Two is the age of separation, individuation. Zero is the age of birth in most human beings. So, the infant between the ages of zero and two has many needs. The infant is hungry. The infant is wet. The infant is thirsty. The infant wants a hug. The infant wants attention. The infant has object impermanence, object inconsistency. He's afraid to lose mommy if she leaves the room. So, he needs her presence all the time and if she's not present, he's terrorized. The infant needs love and empathy and acceptance and warmth, tactile input, etc. Infants have many needs, even more in many ways than others. And the problem of the infant at these ages, well, with one or two notable exceptions, the problem of the infant is that the infant is unable to verbally formulate these needs and these thoughts. These needs are experienced as partly cognitive, partly instinctual, partly reflexive, partly animalistic, partly dimly human, partly respondent, the responses to drives, partly, you know, it's a very hazy, fuzzy need. And because it's hazy and fuzzy, because it's so diffuse, because it's so pinpointed and accurate and exact and precise and goal-oriented, because the infant has no information about the environment. So, he doesn't know that being hungry means food. He doesn't know what is food. He knows hungry, not hungry. So, it's a binary, these are binary states. And what separates hungry, separates hungry from not hungry, is mommy. So, the only object out there that he's dimly aware of is mommy at this stage. And he has no knowledge, so he cannot formulate strategies. He cannot say to himself, well, right now I'm hungry or chapped, so I'm going to get me some hamburger. He's not going to say this, because he doesn't know what is a hamburger. He doesn't know that he's hungry and he doesn't know what is all chapped, which I assume many of you also don't know. So, the baby is in trouble, because he has these overriding, life-threatening needs.  These are life and death issues. And he doesn't have the language, he doesn't have the basic tools, but not only the language. He doesn't have the awareness, he doesn't have the ability to formulate strategies, because he has zero self-knowledge and zero knowledge about the environment and in the state of total ignorance, it's very, very difficult to survive.  You don't know what to do with this motivation. It's like, I'm not comfortable, I need to be comfortable. I am not, I need to be. Not, yes, no, yes, being un-being, being hungry, not being hungry. This is very, very primitive, very basic. So, the child confuses his needs with his self. At this stage, zero to two, even if the British object relations scholars are right and the baby has an ego, it's a very primordial, primitive, rudimentary kind of construct to be in the process of becoming. It's not something which is remotely comparable to the ego of a child of age six, let alone an adult of age 60. So, the ego of the baby, and there are many, many scholars who dispute even this. They say the baby is born tabular, rasa, has no ego, has nothing, no self-structures. Everything is imported from the outside. We'll come to it in a minute. So, when the baby experiences anything, he tends to identify this experience of discomfort, of need. He tends to identify this with himself. In other words, the baby becomes his needs. The baby becomes his discomfort. The baby becomes these binary states, hungry, not hungry, thirsty, not thirsty, wet, dry, mommy here, mommy not here. There's nothing else.  All that exists are these needs, and they are highly structured, they're binary, either or, yes, no, black, white, splitting. So, the baby identifies himself with these needs. His self, his proto-self, his primitive initial self is about needs, it's needs oriented. And what happens when the needs are not met? When the needs are not met, this proto-self, this initial prototype of a self fragments simply. When there's a need that is not met, there is a persistent need. The need is persistent because it's not satisfied, it's not gratified, it's not catered to, so it continues to exist. As long as it continues to exist, the self fragment, the self element that corresponds to this need continues to exist. And if many needs are not met, there are many fragments. Each fragment caters to an unmet, unsatisfied need. Remember, the baby identifies his self with these needs. When these needs are met, they go away. When they go away, there is integration because there's no need to dedicate a part of the self to the satisfied need. There's no call to fragment the self, to cope with multiple needs. If all the needs are met, the self is totally integrated. The self is constellated and integrated via satisfactory, gratifying, non-frustrating, loving, holding, comforting, object-external-object relations. That is the secret of ego formation. For a child to develop a healthy ego, for a child to develop a functioning self, a constellated self, the child needs to experience healthy, satisfactory, loving, embracing, holding, supportive, encouraging, object-relations with external objects. And because the child is zero or one or two, the only external objects are the parents of the caregivers. The importance of these initial object relations with primary objects, that's why they are called primary, cannot be overestimated, cannot be overstated. If the baby's relationship, object relations, if the baby's interactions with the primary objects, mother, father, caregivers, if the interaction with the primary objects is good, is healthy, is functional, these needs are satisfied, they go away. The fragments that used to take care of these needs, the fragments that were misidentified with these needs in the baby's mind, the fragments that were actually needs but perceived as self, these fragments go away because they are no longer needed. The needs are satisfied and they go away by merging and the more they merge, the more the self emerges. Let me recap this, it's not an easy concept. The baby has needs, the baby has zero knowledge, it's totally 100% ignorant, like most politicians. So the baby has needs and doesn't know what to do, he doesn't know what are these needs, he doesn't know anything about the world, he cannot design strategies, he doesn't know anything. He can cope with nothing, he is absolutely, utterly 100 million percent dependent on his parents or caregivers. So because the baby has no access to anything else, no to cognitions, no to developed emotions, not to affect, not to other people via object relations, not to reality, the baby has access to nothing. The only thing the baby has access to are his needs, so he thinks my needs are me, I am my needs, needs are me, me are needs, we are one. And then each need consumes mental energy to satisfy, in order to satisfy a need, in order to meet some need, to gratify, cater to some need, you need to invest, the baby needs to invest mental energy. And he invests mental energy in this need and this is an element of the self. This mental energy is comprised of emotions, of cognitions, of many elements and it is a fragment of the self, it is a section of the self. So each need comes with a corresponding fragment of the self, the self is affected in the need. There is emotional investment, there is investment in the need. So many needs, many self fragments. When the need is satisfied, the fragment is no longer needed, because there is no need, the need is gone. A need satisfied is a need gone. The fragment therefore becomes unnecessary. And so the fragment can merge back into a hyper structure, which is the constellated self. If all the needs are met, there are no fragments, only one unitary self. If some needs are frustrated, if the parents are bad, dysfunctional, if the baby's needs are overwhelming, if the baby feels helpless and hopeless and bad and so on, then these needs and the corresponding fragments of the self will remain active. As long as the need is not satisfied, the need is active and the fragment of the self is active, not integrated. It doesn't go back to the mothership. It doesn't go back to the constellated self but remains detached, dissociated, isolated.  There is the constellated self and it is surrounded by numerous fragments. Each fragment takes care of some specific need. As long as these needs are not met, this is the structure. A core self, which is weakened, broken, damaged, non-constellated, not integrated. Why? Because the needs are not met. So there are many fragments. It is as though this core self imploded and the fragments are taking care of unmet, unsatisfied, unfulfilled needs. The constellation, the integration of the self into a healthy ego, into a healthy self, happens only when all the needs are met via good parenting, good enough parenting. This is satisfactory external object relations. When object relations are frustrating, when relationships, interactions with other people starting with the parents are hurtful, they cause pain, they cause frustration, they evoke aggression, the self remains fragmented into self-states. Each self-state corresponding to an unfulfilled, unmet need. Each self-state has its own set of coping strategies how to secure the need, how to gratify and satisfy the need, how to survive. So coping strategies, cognitions, initially when the baby is one year old to half a year old, two years old, the cognition is very basic. I am hungry is a cognition. So coping strategies, cognitions, emotions, I feel bad, I'm uncomfortable, emotions affects. So we have coping strategy, we have cognitions, we have emotions, they're all embedded in the self-state. And the self-state is not the self. The self-state is separate, divorced from the self. It's out there in deep space, taking care of the unfulfilled, unmet need until such time as the need is met and fulfilled. In the meantime, the self, the mothership, back home, the self is broken, it's fragmented, it's missing parts. And as long as the needs are not met, this would be the condition of the self into adulthood. So coping strategies, cognitions, emotions, they all reside in the self and in the fragments of the self, in the self-state. And the self-states revolve around resolving lacks, resolving deficiencies. They are deprived states. They are states which are focused on deprivation, on lack, on bad. They have negative emotionality and they are invested with aggression. Because Dallad in 1939 taught us in the frustration-aggression hypothesis, he taught us that frustration leads to aggression. So all these self-states are aggressive. They're aggressive, they're dark, they're bad, they're unhappy, they're dissatisfied. And the longer this continues, the more entrenched they become. The more difficult it would be to get them back into the original self and integrate them into a constellated self, for example in therapy. So people with borderline narcissistic, other personality disorders, they have this. This is the situation. They have a wannabe self which is broken to pieces, which is non-integrated, where there's no internal communication, where the signaling is disrupted. And they have like a galaxy of fragmented selves, self-states. Each one with grievances, each one with anger, each one with compulsion to seek the gratification of the need. Each one very self-centered. Each one is, you know, each fragment is concerned with its narrow agenda. It doesn't see the big picture because there's no big picture. There's no constellated self. This is the internal environment of the narcissist and the borderline and paranoid and co-dependent and so on. Now what happens when many needs are not met, when needs generate frustration on a regular basis? At some point, some people internally say to themselves, so to speak, to use a metaphor, say to themselves, okay, I've had enough. My needs will never be met. I'm a victim or I've been dealt a bad hand. I'm an unfortunate person. You know, I have bad luck. This is not going to work. This fragmentation of the self is not working.  My cognitions, my emotions are getting me nowhere. I'm going to withdraw. I'm going to withdraw from the world.  I'm going to ignore all other people. I'm going to sever, cut off all object relations with external objects. At this stage, there is either pathological narcissism which underlies borderline personality disorder and other disorders, not only narcissism or schizoid solution, either narcissistic solution or schizoid solution. There's also a psychotic state, but it's not a solution. The narcissistic solution is an attempt to continue engagement with the world by internalizing the world. By saying, okay, when I go out to the world, it ends badly. So I'm going to internalize the world. I'm going to make the world one of my internal objects so that I can regain a modicum of control and soothe myself and comfort myself. And knowing that I will not be betrayed, abandoned, frustrated anymore because the world is now inside me, is part of me. And I will idealize the world so that I feel perfect and brilliant and godlike. This is a narcissistic solution. And the schizoid solution is to say, I'm going to pretend that there is no world. I'm going to pretend there's only me, no world. I'm going to become so self-sufficient that I will have no needs anymore, any needs. I will have no need of other people, no need of love, no need of intimacy, no need of the world, no need of work, nothing. I'm going to sit at home. I'm going to do my things. I'm going to be happy with myself. I'm going to be my own best company. And both types, the schizoid and the narcissist, are of course auto-erotic in the sense that they invest their psychosexuality in themselves.  Now, of course, there is a psychotic solution, but it's not a solution. The psychotic solution is to say, I'm going to vanish. I'm going to disappear like so many molecules. And I'm going to spread myself thin into the world. This is called hyperreflexivity. But I'm not going to deal with it now, because the schizoid solution and the narcissistic solution are attempts to remain functioning in an environment which is perceived as hostile, an environment which is malevolent, as animosity, an environment which provokes hypervigilance and even paranoia. That's the interface between paranoia and narcissism and schizoid states. So these are attempts to resolve. These are coping strategies. They're very dysfunctional coping strategies, self-defeating, counterproductive. But they are coping strategies. These are desperate attempts to remain sane in a world which is perceived to be insane. The psychotic gives up. Psychotic says, OK, this is so bad. Even going back to the womb like the schizoid does, because the schizoid symbolically goes back to the womb. He closes himself in his apartment and that's it. That's a womb. That's his extended womb. The psychotic says, even going back to the womb is bad, because the womb and the mother who carries the womb contains the womb. They're in the world. I can't be in the world. I need to unbeat. Psychosis is unbeing. Hyperflexivity seems like the big bang. The psychotic suddenly expands outwards, expands outwards and loses any distinction between external and internal, because he eliminates the world by eliminating himself.    The self-states are dormant in people with personality disorders. They're dormant and they are reactive to stressors and that is very similar to dissociative disorders such as dissociative identity disorder, but other dissociative disorders and even dissociative defenses such as depersonalization, derealization and amnesia. They have this in common. In borderline, in narcissism, the self-states are there exactly like someone with multiple personality disorders. And when the borderline is exposed to rejection, abandonment, when the narcissist is exposed to humiliation and to shame, the self-states are activated. They're activated because they respond to needs. Remember that the self-states are fragments of the self, the slivers of the self, the cut-off of the self. They're like sliced salami, the slices of the self and they are responsive to needs. Now when the narcissist is humiliated, when he's shamed, he has a need and the need is to reestablish grandiosity. To reframe what had happened in a way that will not drive him to modification. So then one of these self-states activates to respond to this need. When the borderline is about to be abandoned, about to be rejected, she has a need. She has a need to regulate her internal environment without the benefit of an intimate partner who is about to abandon her. So she activates a self-state. The self-state caters to this need by becoming a secondary. The self-state is a secondary psychopath and secondary psychopaths don't need regulation. So the secondary psychopath, self-state of the borderline is exactly this, a psychopath. And there's no problem with regulation, it solves the need. So self-states are needs oriented when the need arises, they're activated. But as opposed to multiple personality disorder and most conditions, most dissociative disorders, not all, but most. As opposed to these, in people with personality disorders, the self-states are permeable. Permeable means the dissociative wall, the dissociative partition of firewall between one self-state and another is very, very permeable. Self-states in people with personality disorders communicate.  They are not coordinated, they're conflictive actually in most of the cases, they're polarized. As Schwartz called it, they're polarized. But they are, they exchange information. This is the closest I can see. They're informed, they're all informed. And of course the self, the fragmented, broken, damaged, non-constellated, non-integrated, identity-disturbed self, whatever is there, the little that is there, which is not a core identity, it's not stable across time, it's diffused still, there's something there, something primitive and basic. This part which passes for self in healthy people, this part is also informed. This is a lot of exchange of information. The minute there's a hint of stress or a hint of stress, a hint of frustration, of hurt, of pain, of negative emotion, of emotion, of modification, the minute there's a hint of something, of the secretary threat, paranoid threat. The minute there's something that creates disequilibrium, disturbs the homeostasis. That minute one of the self-states, the relevant self-state, the self-state that can take care of the need of the problem is activated. During hibernation when these self-states are not needed, they are perceived as internal objects, which they are. They are not a part of the state, they are not a part of the self, I'm sorry, the self-states are not parts of the self. They have divorced the self, they are fragments, they are spread all over the deep space of the narcissist's psyche, of the borderline psyche. So they are not by any extension parts of the self, they used to be parts of the self, now they are just fragments. So they are perceived as internal objects, and there are very interesting dialogues going on between these internal objects, and the selves between internal objects, other internal objects, and the self-states. So for example in a borderline you could have a mother interject, a sadistic inner critic, which is essentially a mother interject. Talking to a secondary psychopathy self-state, and so the mother could chastise, could criticise the psychopathic self-state as bad, unworthy, corrupt evil, and that would create a lot of guilt and shame after the fact. After the secondary psychopath takes over, when it's no longer needed and it recedes, the borderline will experience guilt and shame, which is the outcome of the dialogue between the sadistic inner critic mother interject, and the secondary psychopathy internal object. They are both internal objects. So there is a lot, for example in the narcissist, you could have an interject for example of a very influential teacher. You could have an interject of this influential teacher telling them the self-state of the narcissist, the grandiose self-state in the narcissist, telling this grandiose self-state it's not okay to be grandiose.  So there could be a dialogue between the grandiose self-state, which I remind you is sliced off the self, is not part of the self. In narcissism, ironically, in pathological narcissism, narcissistic introversion, which is healthy, had failed. Narcissism in narcissistic people had failed, not succeeded. When narcissism succeeds, it becomes healthy narcissism. When narcissism fails, for example, in narcissistic introversion, in Jung's theory, or narcissistic self-structures, in Coghurt's work. So when narcissism fails to be invested properly, when it fails, there's pathological narcissism.  And these dialogues are going on all the time, it's amazing and you can bring them out in therapy. You can make the patient aware of these dialogues, which I do in cold therapy. Okay, Shoshanim, I hope you answered some of your questions. Feel free to pose others before you do. Make sure you search and research my channel, because I don't take kindly to wasting my time. To search my channel, you go up, there's a magnifying glass symbol, that's the search box.  Make sure you watch these videos before you post questions. If you do post a question, which I hadn't answered in any of my previous videos, any of my 700 previous videos, I'd be delighted to respond. I usually do, I respond to questions, new questions, questions which I didn't tackle in any of my videos. However, I become seriously nasty and obnoxious. When you waste my time with questions, the answers to which you can find in 20-30 videos that I've made. Because this is entitlement and this is abusive conduct. Got it, children? Okay kiddos, have a nice day.


He lost his father, lost his best friend, lost his lover, and he lost his mentor, and later he even lost his patented sharingan. Kakashi Hatake was born in the hidden leaf. His mother unknown and his father Sakumo Hatake, Konoha's white fang, a ninja who was once as powerful as the Sanyin themselves, but later disparaged by his comrades for choosing to save a friend over the mission. Kakashi had the intelligence and ability of attuning at 5 years old. When he was an academy student, he entered the Anbu Black Ops at 12 years old and was by far the most powerful ninja in his class, but he was distant. Kakashi didn't say much and he didn't care about much. But this is because Sakumo committed suicide and Kakashi didn't have much of a childhood. He didn't get to enjoy life as a kid and he didn't carry the same innocence that the other kids carried. He was forced and forced himself to grow quickly, almost like he was running away. But it seemed like that would only make things worse. The self dependent Chunin was later forced to have teammates, Obito Uchiha and Rin Nohara, and though he didn't show it he cared for them. Then Obito's life was quickly taken by the hands of falling rocks. Obito gifted his friend with his left eye, the Eye of the Sharingan, as a dying gift, and with the final breath Obito asked Kakashi to take care of Rin, who carried a two-tailed beast inside of her.  And though Kakashi denied her request, Rin threw herself in the way of Kakashi's attack, as he impaled her heart with a lightning blade. And with this, the young Jonid had lost both of his teammates, his father, at the ripe young age of 12. Again, 12 years of age and he had already lost his father, his friend, and what many believed to be his lover. Kakashi would become depressed and later joined the Anbu Black Ops. In the Anbu, the Jonin released his rage and emotion through his hands and through his talent. He displayed a cold-heartedness and ruthlessness in the Anbu, and he wouldn't talk to his teammates for days at a time. But his successes were noted, as he rapidly rose through the Anbu's ranks. Kakashi's hardships would not end there. When the nine-tailed fox was set on the village, the Anbu was prohibited to defend the village, only being deployed to protect its citizens. The demon fox was slain, but at the hands of his mentor, Minato, the fourth Hokage, another person who Kakashi had opened himself up to, and that he would lose. At this point in the tale it becomes Naruto's story, Kakashi's grievance had not ended. The copycat ninja was chosen by the third Hokage to be his right hand, who was later killed by Orochimaru, and finally Kakashi loses his sharingan at the hands of Madara Uchiha. Kakashi's story is one of incredible resiliency, but a story of faith and teamwork as well, and I believe that two different things motivate the copycat ninja, the belief of his own abilities and later friendship. I call his story one of faith, but one of the saddest stories in the Naruto universe. As Kakashi could have blamed the leaf for ostracizing his father, he could have turned against them for forcing his father to take his own life, but somewhere inside of him, Kakashi had forgiveness, and would later lay his life down for the leaf, even assuming the position of its leader, the sixth Hokage. And though Kakashi blames himself, he holds the burden of these people, which propels him forward to take on each day as they would, and in their honor, the mindset and the teamwork of the White Fang, Obito's hard work and love of life, Rin's kindness and love, and Minato's ability. When Kakashi's father died, he was motivated by his own ability, the ability to become better than his father not only in status, but in talent and skill as well. The young Kakashi didn't even want to be associated with him, stating that he would follow the rules unlike his father, little did he know the White Fang was so honorable. And then when Obito died, it is at that instant that Kakashi understood why his father sacrificed the mission in order to save a teammate. It is at that instant that Kakashi realized that the people around him were much more important than any mission, and that the survival of the team should always be the number one priority. And while he doesn't overtly say it, he cares immensely about the people around him. As the village raised him, and through team 7, my guy Kuranaya Asuma, and everyone else, he believed that he could inspire a culture of teamwork, a teamwork that he wished he had with his own team. Though Naruto was motivated by other people as well, Kakashi is definitely credible in the motivation that Naruto has to pursue his best friend to the ends of the earth in order to bring him back to the light, something that Kakashi wishes he could even have the opportunity to do. The copy ninja is the pinnacle of resiliency and persistence. Kakashi Hatake is the man who lost everything, and though death has silenced him, he speaks profoundly with his actions, and with a smile. Those who break the rules are scum. That's true.


Back on the Sportsmax zone, we're switching our attention now to the sport of Kings. There has been much criticism of horse racing in Trinidad and Tobago in recent years, with many stakeholders expressing dissatisfaction with the state of Santa Rosa in Arima. Now one of the country's finest trainers, 20-time champion John O'Bran, is considering taking his talent outside of the country. O'Bran says he still loves the sport in the Twin Island Republic, but thinks it may be time for a change if things don't improve. Well, my hope is that racing in Trinidad recovers and finds its legs and gets back to where it was maybe 10 years ago, but you know, in the back of your mind, you always think that they have to be exploring other possibilities. And at this stage, my heart is still in Trinidad, but my thoughts could be abroad. Yeah, well, John O'Bran now joins us live via Zoom to talk more about that statement, which he gave us about a week and a half ago. John, we understand the issues in Trinidad and Tobago's racing at the moment. A stark reality is that your Dabu winner Momentum back in 2014 had a Dabu purse of 500,000 TNT dollars. Your Dabu win this year within the headlines was 115,000 dollars in purse. So things have nosedived in Trinidad and Tobago with regard to the purses in TNT. How bad is it and how frustrating it is for you as a trainer who has success and knows, you know, what the financial rewards were compared to what they are now? Well, the answer is you are aware we prior to COVID and in say 2014, 2015, we would have maybe between 36 and 40 races a year. And in this year, we're going to have 12, which is the stark reality of it. So you told us in that interview that you would not rule out leaving Trinidad and Tobago. What would have to happen for that development? Well, as I said, I love horse racing, but I also my heart and the able string is buried in Trinidad and I wouldn't I wouldn't really love to leave. But if there is no horse racing, we'll have to definitely have to explore possibilities elsewhere. So is there a possibility that racing could crash in TNT totally because it's it's in a coma at the moment? Is it possible that it could die? Well, at present, it's in the ICU and it could go one way or the other. And the all indications at this stage that we slowly sink in down. So we have to keep all our options open. The environment is not not not conducive and the regulations rule in recent local racing is is is poor. Yeah, and John, I was looking at one of the last purses, you know, as well as the number of horses that took part in that particular race. And it was really, really demotivating because when you think back about horse racing in Trinidad and Tobago and the rich history that horse racing had, you know, growing up, my grandfather really liked horse racing. And I would go down to the Arima race track just to support the turnout was massive, a lot of horses on the race cards. What do you think has been one of the reasons for this downturn and, you know, this dying of the industry? Well, there are a number of reasons, but it's a cumulative effect. What what really happened was that we we are we are dependent. We were dependent over the 20 years or 30 years on the revenue earned by the betting levy board, which where they get the revenue by a 10 percent taxation of the private betting shops and of local racing. And in there was at one time, there were 20 private betting shops. We are now presently down to six. So the drastic drop in revenue has created there is no revenue to support local horse racing. And I think that there is the reason why the betting shops reduced from 28 to six because of the proliferation of private members club running on casinos and also the online betting, which which is which is available to everybody worldwide and there is no revenue to get from it from for the for the from the betting levy board. The betting levy board gets no revenue from online betting. And John, saying that, you know, you made that comment about thinking about possible options. Have you thought about where maybe when I wouldn't like to say because it may compromise a lot of opportunities because there are there are a number of opportunities at this time. We see that a lot of riders have been steadily leaving TNT. Brand Boonram Singh, John, who writes for your have written has written for you is now in Canada doing well, actually won a stakes race this past weekend. The jockey colony in Trinidad and Tobago has also suffered in recent years, hasn't it?  We had I think the last race we had 12 horses in and one guy had to scratch his horse because there was no jockey available to ride it. Well, the good thing is for the next couple of months is that the guys the guys from Canada and a number of them have returned and even Brian himself is back in Trinidad. I think he came in last night and you may find him right in the next race day, because he is things and as you know, we are down south close. I think sent three mile closes sometime in early November. Yes, one thing actually, yeah, that's entry downs. All right, John, we have all been impressed with the work you have done as a racehorse trainer in Trinidad and Tobago. We know that you're also a pilot by profession, probably retired by now. But we would hate to see you leave Caribbean horse racing. So let's hope things improve in Trinidad and Tobago. And that racing is revived in some way, shape or form to keep John O'Bran at Santa Rosa Park. Well, I didn't say it was outside of the Caribbean. We're getting some hints, Lance. I said that deliberately, you know, because I was hoping that you would respond and you did. All right, John, well, we'll be in touch. And as we said, you know, as racing people in the Caribbean, you know, we have all embraced the K-Manus Park, Garrison Sabana and the Santa Rosa Park racing. And it's sad what's happening in TNT at the moment. Let's hope that things can improve. And we'll see racing revived in TNT. Thanks, John. Thank you very much, Lance. Have a good day. Yeah, back with more on the Sportsman Zone after this.


Okay, so next is we are going to do square plus a square minus x square root. Some more special matrices by parts, okay, and their results are so many places. So we are not on the, and the root of it would become ac theta, d theta. So when you substitute it, it becomes ac theta. So ultimately we will get the approach solving this problem. Find the x square root, and then again...


Hey, it's been a bit it is currently like six o'clock in the morning. It's not six o'clock It's like 6 30 6 45 it might be seven but today's my first video back in in quite a while And I have some stuff to tell you guys first of all is my birthday, which is cool I've been I've been having a lot of stuff happen in life Recently as a lot of you guys probably saw on Twitter, but yeah I took I took a little bit of a break from making videos and doing anything which is funny because I stopped making videos Right after I was like, yeah, it's been really fun doing more daily stuff. Whoopsies, but yeah, it's my birthday I'm 26 today getting booted off my dad's health insurance 26 isn't a very exciting year and to be honest I kind of forgot that it was going to be my birthday this week and then I woke up this morning and I was like, oh, yeah It's my birthday. I guess but other than that I have some very exciting news and some stuff That has been in the works for a long time and some stuff that a lot of you guys have wanted Sorry, if the camera is shaking Spencer just bumped the tripod but something that's been in the works for a while and something that Some of you guys have been asking for not all of you because it doesn't necessarily benefit all of you But I'm going on tour again, and I'm really excited because this time I'm going overseas, baby. That's right. I am doing a EU slash UK tour you can go to I have to do this dot show If you want to look at where I am going, I'm going to be here here here here here Why am I not saying them out loud? Because I'm using my phone to film this and I can't look at the list and I can't remember all of them Yes, but yeah, I'm I'm going on tour in Europe and the UK And a little bit of Scandinavia as well Starting on January 17th, so all of you who are who are overseas who are missing the tour Don't worry I'm coming. I'm coming to you, baby, and I'm really really really excited doing doing the tour and doing the show was like One of the best moments of my life. Honestly, it was so much fun It was so fulfilling all the people that I got to work with were amazing. It was so much fun seeing all of you guys and so I'm I'm really really excited to to do it all again and And do it in some really amazing beautiful places I'm super excited to be going back to Europe in the UK the last time that I was there It was the last time that I was there doing your welcome If you are in the UK if you're in Europe if you're in Sweden at all God, I have to do this dot show and can check out Where I'm gonna be so tickets go on sale at 10 a.m. Local time this Friday So they are not currently on sale. They are not currently on sale. They go on sale on Friday 29 the 28th They go on sale Friday the 28th This coming Friday at 10 a.m. Local time so whatever time zone you're in at 10 a.m They will be available for you because we're going overseas all the shows are a little bit smaller So tickets will probably sell a lot quicker because the venues aren't as big as they were here in the US So maybe keep that in mind But I'm super excited. I'm so excited to do the shows again I'm so excited to to bring the show back to life I'm so excited to like be on stage again because I really really love Being on stage. It's really fun It's like one of my favorite things to do. So I'm really excited. I hope that this announcement wasn't Shitty for you Because I tweeted because I haven't uploaded it a month over a month And so I was like I have an announcement and a lot of people were like I wonder what it is So if you are in the US, you're probably like, huh, well I already saw the show or well And maybe I'll take a trip to Europe. It's a great excuse to go to Europe or London or other places that I can't currently remember put it on her calendars Friday the 28th 10 a.m. Local time tickets go on sale and this I'm pretty confident will be the last leg I'm sorry the rest of the world So if you haven't seen the show and you really really really really really want to see the show This might be the last time. I'm not trying to guilt trip you. I'm just saying that this might be the last time That's all I'm saying. That's it. That's that's the announcement. I'm going on tour again so thank you guys so much for for Chilling with me this last month and just being super patient I think I'm gonna do a stream on Twitch this morning if you feel like stopping by if you feel like Saying hello. It is my birthday. So, you know, it'd be shitty if you didn't come But I'm just gonna hang out for a bit But yeah, I hope to see you guys in Europe in the UK Wherever I see you let's go on tour again, baby


Hello and welcome to lecture number 21 of this lecture series on Introduction to Aerospace Propulsion. We have been discussing over the last several lectures on basic aspects of thermodynamics including some of the basic cycles which are which form very important aspects of engineering analysis and our day to day use as well. And we have also had several tutorial sessions during which we have solved some problems related to basic thermodynamics as well as in the last lecture we have solved some problems related to cycle analysis of some of the cycles like the auto cycle, the diesel cycle and the Erikson and the Brayton cycles. And what we shall be discussing today is a very different topic in some sense in as compared to what we have been discussing in the last few lectures. And but of course, they will the discussions of today's lecture will also be an important aspect of thermodynamic analysis of certain systems which involve mixtures of gases or in processes which involve vapor water vapor for example. Like if you have to use Rankine cycle for a steam power plant how do you carry out a thermodynamic cycle analysis of such a cycle because Rankine cycle involves water and steam and therefore, we need to calculate properties associated with water and steam. And so today's lecture is aimed at understanding of properties of water known as pure substances as well as mixture of ideal gases and real gases and so on. So, what we shall be discussing in today's lecture of the following we shall be talking about properties of pure substances what are meant by pure substances. We shall then be discussing about what is meant by compressed liquid saturated liquid saturated vapor superheated vapor and so on. We shall be also discussing about what is meant by saturation temperature and pressure then we shall be talking about property diagrams of pure substances property tables composition of a gas mixture then we shall talk about PBT behavior of gas mixtures ideal gas and real gas mixtures and properties of gas mixtures. So, these are some of the aspects that we shall be discussing in today's lecture which is primarily aimed at understanding of properties of pure substances. So, what do we primarily mean by a pure substance because that is going to be our topic of discussion for today's lecture. Now, a pure substance is one which has a fixed composition throughout the process and so such a such a substance is referred to as a pure substance. Examples of pure substances can be water or gases like nitrogen oxygen helium and so on. So, these are certain substances which will have the same composition throughout the process and that is why they are called pure substances. And a mixture of one or more phases of a pure substance will still remain to be pure substance as long as the chemical composition of individual phases of the mixture does not change. That is a mixture of water and vapor that is water vapor will still be qualified as a pure substance because the chemical composition of neither water nor water vapor changes during the process. So, as long as that is maintained then even a mixture of different phases of the same substance which is a pure substance will still be called as a pure substance itself. And so a substance which has a fixed chemical composition throughout is called a pure substance. Examples are water nitrogen helium and so on. A mixture of two or more phases of a pure substance will still be a pure substance as long as the chemical composition of all the phases is the same mixture of ice and water and so on. Properties of water and its phase and its different phases form a very important part of analysis because in different systems engineering systems one would come across use of water and its different phases like ice or steam. And therefore, analyzing different properties of water and its different phases will be a very significant part of an analysis of any system which involves water and its phases. And therefore, it is important for us to understand the significance or importance of water and its different phases which is why we are basically trying to understand properties associated with water and its different phases. So, before we try and understand those properties we need to understand certain terms associated with how water behaves at different states or phases. Now, if we consider water which is at a state which is far away from being vaporization that is water which is or a liquid which is at a state which is not about to vaporize is known as a compressed liquid or a sub cooled liquid. So, water or any other liquid where it exists in a state wherein it is not going to vaporize at all such a state of water or that liquid is called compressed liquid or sub cooled liquid. For example, water at a temperature of 20 degree Celsius and 1 atmosphere is a sub cooled state because water is not at a state of evaporation at a 1 atmosphere because we all know that at 1 atmosphere water boils at 100 degree Celsius. A liquid that is about to vaporize is called a saturated liquid that is liquid which is in a state that it is just about to vaporize is known as a saturated liquid. And a vapor on the other hand which is about to condense is called a saturated vapor. So, vapor which has reached a state wherein it is about to condense is known as saturated vapor. And a vapor which is not about to condense that is it is not a saturated vapor is called a super heated vapor. That is the vapor happens to be in a state where even some amount of cooling does not cause it to vaporize or condense is known as super heated vapor. That is when you have vapor which is at a temperature and pressure which is not close to the saturation temperatures then that vapor is known as super heated vapor. So, what we have discussed are compressed liquid or sub cooled liquid wherein the liquid is not about to vaporize. A liquid which is about to vaporize is called a saturated liquid. And a vapor which is about to condense is called a saturated vapor. And a vapor which is not about to condense is known as super heated vapor. So, what I will do now is to illustrate all these different states by some example we will use water as our example because that is the most common liquid that we come across in engineering systems. So, if you look at different states of water let us look at state 1 for example, at state 1 water is at a pressure of 1 atmosphere and 20 degree Celsius which means that the water is not about to vaporize. It is not at a state that it will begin to vaporize. Therefore, this particular state that is state 1 is known as the compressed liquid state for water. Now, we consider state 2 that is we continuously as you can see we are adding heat to the system. As we add heat at constant pressure that is the pressure remaining constant now the temperature increases. At the state 2 temperature of water is now 100 degree Celsius pressure remains 1 atmosphere. So, this state is known as saturated liquid state for water that is water is at a state now that it would start vaporizing any minute now or that is at any moment the water would start vaporizing which is why it is called saturated liquid. State 3 is a mixture of saturated vapor and saturated liquid because as we continue to add heat at 100 degree Celsius water will start vaporizing provided pressure is 1 atmosphere and once it starts vaporizing you can see there will be one part of the system which consists of a vapor of water and second part consists of saturated liquid and so we have a mixture of saturated liquid vapor. So, this is saturated liquid vapor mixture that is state 3. Looking at state 4 we again add heat continuously till a point where there is no more water left in the system. And so at 1 atmosphere and 100 degree Celsius if you have water vapor then that is known as saturated vapor because if you start removing heat water will on that is vapor will immediately begin to condense. So, this is known as saturated vapor state. State 5 is if we again add continuously heat at constant pressure that is 1 atmosphere then we have higher temperature of the vapor which is not close to its condensation temperature and this is known as the super heated state of water or vapor. So, state 5 is super heated vapor. So, what we have seen are 5 different states of the same substance the same pure substance that is water. State 1 was of water at temperature and pressure which is far away from its vaporization temperature that is known as sub cooled or compressed water state. Second state is if you heat water up to 100 degree Celsius at 1 atmosphere water is at a point that it may begin to vaporize any moment that is. So, this is known as the saturated liquid state. The third state is as you again add heat water will begin to evaporate. So, you will have a mixture of water and vapor at 100 degree Celsius and 1 atmosphere. So, this is known as the saturated liquid and vapor mixture. Fourth state is that we have only vapor which is at 100 degree Celsius for water and so that state corresponds to saturated vapor state because the vapor will begin to condense at any moment. And last state is at a temperature which is far away from the condensation temperature and that is known as the super heated vapor state wherein the temperature is far away from the condensation temperatures. So, for water temperatures much beyond 100 degree Celsius at 1 atmosphere would be super heated state of water. So, what we shall do now is we know that we have seen 5 different states of water. Let us plot the temperature and volume. Let us plot this particular process that we have seen of adding heat to water. So, as to get different states or phases of water and plot them on a constant pressure line. So, what we have seen is in all the 5 different states that we have identified pressure remains a constant that is 1 atmosphere. So, on a constant pressure line we will plot this property on temperature and specific volume coordinates. So, on T V coordinates or T V diagram temperature and specific volume if you were to plot this particular process that we have seen which is basically from state 1 to state 5. This is a constant pressure process it is constant pressure at pressure equal to 1 atmosphere. Water was initially at state 1 at 20 degree Celsius and as you heat water at constant pressure this is how the process proceeds up to state 2. So, this is the compressed liquid state because at these states water is not in a position that it will begin to vaporize. At state 2 is when you have saturated liquid that is 100 degree Celsius. So, water is in a position that it will begin to vaporize. State 2 corresponds to saturated liquid state and state 2 to state 3 is saturated mixture where you have liquid as well as the vapor and after it reaches state 3 and it goes to state 4. So, any state in between 2 and 4 which is equal to state 3 that is saturated mixture state after it reaches state 4 we have the saturated vapor state that is we have only vapor which is saturated that is it may condense any moment. Further addition of heat at constant pressure increases the temperature it was 100 from all the way from state 2 to state 4 and as we increase the temperature we have process going from state 4 to state 5 and this is the super heated state that is we have now temperatures which are much higher than the condensation temperature. So, the vapor reaches a temperature of 300 degree Celsius let us say that was at state 5. So, state 5 is the super heated vapor state. So, any point in between 4 and 5 corresponds to super heated vapor. So, 4 5 is the super heated vapor state. So, this is how you would plot this process which is basically heating of water from sub cooled state that is compressed liquid all the way up to super heated vapor state. So, as you heat from state 1 to state 5 water passes through a series of different states which involves sub cooled state saturated liquid state saturated liquid vapor mixture saturated vapor and the super heated vapor. So, as we continuously heat at constant pressure water passes through these different phases and we have discussed 5 different states of water which correspond to different states of water as well. And so, we can plot the property diagram on a constant pressure scale between temperature and specific volume and we see the how we can we can actually see the variation of the different properties of water as it passes through these different states. So, property basically the temperature in this case was changing, but the pressure was kept constant at 1 atmosphere. So, it is also possible that you can change it the other way around that is we can also change pressure that is as you keep changing pressures the characteristic curve that we have just seen will also change because this is valid only for pressure is equal to 1 atmosphere. For any other pressure we know that the boiling point of water the condensation point of vapor will all be different which means that as you plot this for a different sets of pressures and temperatures we should be able to get on TV scale this temperature volume scale a series of these constant pressures lines along which water would continuously change its phase. And so, this is what we shall try and do and see different property diagrams or scales in which we can see how the properties of water would change. Now, in order to do that that is because temperature of water that is temperature at which water would start boiling also depends upon pressure it is a strong function of pressure. And so, if we fix pressure the boiling temperature is also fixed. So, at a given pressure the temperature at which a pure substance changes its phase is called the saturation temperature or T sat as it is represented. So, once you fix the pressure what is the temperature at which the temperature of the phase changes that is basically known as the saturation temperature. Similarly, the at a given temperature the pressure at which a pure substance changes its phase is called the saturation pressure. So, saturation pressure and temperature are both functions of each other in some sense that is if you fix the pressure then the temperature at which a substance pure substance changes its phase is known as the saturation temperature. And as you fix pressure the temperature at which the property of the pure substance changes its phase is known as the saturation temperature. So, saturation pressure and temperature will form a very important aspect of analysis of pure substances which continuously evolve and change their phase. So, in the previous picture or diagram which had shown variation of the properties along a constant pressure line. If you were to plot multiple number of these pressures what we get is a series of points that is if you join all the state 2's and state 4's we get a saturation line on one side we have a saturation liquid line on the other side we have saturation vapor line. And eventually this will meet at a particular point which is known as the critical temperature or critical point. So, let us plot a series of these lines on T V diagram that is temperature and volume diagram in the previous slide or 2 slides from here we had shown I had shown you a line which is looking like this constant pressure line compressed liquid saturation liquid mixture of saturation liquid and vapor saturation vapor here and superheated vapor after this. So, what if I plot this for multiple pressures. So, if I increase the pressure P 2 which is greater than P 1, but is equal to a constant we get a line like this that is for higher pressures the temperatures will also now be different. And so, as you increase the pressure the boiling temperature of water also changes you must have learnt in your school days earlier on that if you go to a high altitude place water boils at a lower temperature that is it boils at temperature lower than 100 degree Celsius. At higher altitudes we know the pressure is lower and therefore, water will also boil at lower temperatures that is if you were to plot below this let us say this is atmospheric pressure one atmosphere which is what we did last time where in water boils at 100 degree Celsius. So, if you were to plot this for let us say less than atmospheric sub atmospheric pressure which will occur at high altitudes water will boil at lower temperatures. Similarly, at higher pressures water boils at higher temperatures. So, you can see as you if you plot multiple number of these pressure constant pressure lines what we can see is and we join all these points locus of all these lines points which join state 2 which was the saturated liquid state of water. We get a saturated liquid line and on the other hand if you join all state force which was saturated vapor state we get a saturated vapor line. And both these lines meet at a point which is known as the critical point and all points on the left of the saturation line correspond to the compressed liquid state all those points on the right hand side of the saturated vapor line corresponds to the super heated vapor state. And those which fall within this curve corresponds to a mixture of saturated liquid and vapor. So, this is basically a critical diagram which also shows how you can achieve a critical point when you were to plot different states of water for different pressures. And so in general if I were to plot this for pressures which are higher than the critical pressure which means that if you have a constant pressure process which has a pressure higher than let us say the critical point that is p greater than p critical then what basically happens is that super critical pressures where pressure is greater than the critical pressure there is no distinct phase change. Because phase change occurs only during the process which is below this curve this is basically indicating the phase change process. So, after the critical point there is basically no distinct phase change process that takes place. So, at pressures which exceed the critical pressure one cannot see a distinct phase change or a boiling process. Whereas, at pressures which are below the critical pressure there would be a very distinct phase change process or a boiling process during which liquid becomes vapor and so on. So, there is a distinct phase change that occurs for processes which occur at pressures which are below the critical pressure. And for pressures which are higher than the critical pressure there is no distinct phase change or boiling process that we can see during change of phase of a pure substance. So, we have now plotted the phase change process in terms of temperature and specific volume coordinates where we have seen a constant pressure on a constant pressure line how the different properties can change and how phase water changes its phase from or water how it water changes its state from sub cooled state to saturated liquid state to mixture of saturated liquid and vapor then saturated vapor and the super heated vapor. So, the locus of all the saturation lines which include the saturation liquid is known as the saturated liquid line. And that was if you join all the state 2's of a constant pressure lines we get saturated liquid line if you join all the state 4 lines we get the saturated vapor line eventually both these lines meet at a point which is known as the critical point. And so for pressures which exceed the critical pressure one cannot really see a distinct phase change or a boiling process. So, what we will do next is to plot phase change process on a P T diagram that is pressure and temperature coordinates and see how the variation looks like. On pressure and temperature coordinates if you were to plot the phase change process. So, here we have the solid state, the liquid state and the vapor state. So, if you were to look at a process where the pressure and temperatures are changing for pressures and temperatures below the triple point triple point is by definition the point at which all the three phases coexist in equilibrium that is solid liquid and vapor. And for water the triple point is 0.01 degree Celsius. So, a line which basically demarcates the solid from the vapor that is at pressures which are lower than what corresponds to the triple point or temperature as well as pressure the process which will occur would basically be a sublimation process that is solid would directly become a vapor without becoming a liquid that is if you have pressures and temperatures which are below that of the triple point. Then if you take up ice for example, ice will directly vaporize into water vapor without actually melting. Melting would occur only at temperatures and pressure which correspond to what is shown here. And there are two melting lines shown there are substances that expand on freezing and there are substances that contract on freezing. And for example, water is a substance which expands on freezing. And so the melting line for water is which is basically has a negative slope whereas, those substances which contract on freezing have a positive slope of this melting line. So, water will follow this melting line and if because it is temperature and pressure is above the critical point above the triple point. So, solid ice would melt and become liquid and as we have seen this is basically the vaporization line where on further addition of heat water would become vapor. And you also have the critical point shown here. So, critical point was also defined in the previous diagram here. And this is that was of course, on temperature and volume coordinates this is on pressure and temperature coordinates. So, this is basically a pressure temperature diagram of any pure substance. And difference between different pure substances will come in the location of the triple point as well as the critical point because that is different for different pure substances. For example, for water the melting line is slightly different from the melting line for substances that contract on freezing and so on. So, there are three distinct phases that you can see here the solid phase which is between the sublimation line and the melting line. The liquid phase is between the melting line and the vaporization line. And the vapor phase is between the sublimation line and the vaporization line. And the point at which all these three phases coexist is known as the triple point. So, we have plotted the properties on different scales on temperature volume pressure temperature and so on. And it is also possible to plot these diagrams on a three dimensional plot which is known as the PVT surface pressure volume temperature surface. And so, which is basically a combination of pressure volume pressure temperature and temperature volume coordinates and so on. Now, the properties of different substances of pure substances are either plotted in terms of these coordinates or you can also see them in terms of a tabular format. So, there are tables associated with properties of pure substances because the thermodynamic relations for different substances can be quite complicated. And so, calculating each of the properties like enthalpy, entropy, etcetera at different pressures and temperatures can be quite involved. And to avoid that, there are standard property tables available wherein for given pressure and temperature one can determine the different properties like energy, the entropy and enthalpy and also specific volume of different pure substances. And so, if you look at the property table which is something we shall be discussing now, basically the properties are in the form of tables. So, there are different property tables available for different substances and properties of water are usually referred to as the steam table where we get different properties of water, liquid water vapor as well as superheated steam. In all these tables, subscript f is used for denoting properties of saturated liquid and subscript g denotes properties of saturated vapor. And also f g denotes the difference between saturated vapor and saturated liquid values of the same property. So, in these tables you would find subscript f which corresponds to properties of liquids that is saturated liquid, subscript g denotes properties of saturated vapor and subscript f g denotes the difference between these two of the same properties. So, for example, h f that is h subscript f basically corresponds to specific enthalpy of the saturated liquid. H subscript g is the specific enthalpy of the saturated vapor. And therefore, h f g is the difference between h g and h f that is h f g is equal to h g minus h f that is basically the difference between specific enthalpy of the saturated vapor and specific enthalpy of the saturated liquid. If you recall in the property diagram I have shown that, but process from 2 to 4 corresponds to the phase change process. And therefore, the difference between enthalpies of the vapor and that of the saturated liquid is basically the enthalpy of vaporization or latent heat of vaporization. That is the difference between h g and h f is the difference between the specific enthalpy of the saturated vapor and specific enthalpy of the saturated liquid, which means the difference between the two basically corresponds to the amount of energy required for carrying out this phase change from liquid to vapor. Therefore, h f g is basically the latent heat of vaporization or enthalpy of vaporization as it is also sometimes called. Now, so within this saturation curve that we have drawn where we have a mixture of saturation liquid as well as vapor. We know that there is some fraction of liquid water present there is some fraction of vapor present. So, we will now represent this fraction by what is known as quality that is what is the quality associated with this particular vapor and liquid mixture. So, quality which is usually denoted by symbol x quality x is basically the ratio of mass of water mass of what vapor to the mass of liquid that is quality x is basically the ratio of mass of the vapor present to the mass of liquid present. Therefore, quality has a value which ranges from 0 to 1 which means if quality has a value of 0 it means that the mass of vapor present is 0 and liquid. So, the entire mass is basically the mass of liquid. So, its quality of 0 corresponds to saturated liquid state and quality of 1 corresponds to saturated vapor state because it is at that state where the entire mass corresponds to the mass of the vapor itself. And so any value of quality which is between 0 and 1 corresponds to mixture of saturated liquid and vapor state. So, quality x is basically defined as the mass of vapor ratio of the mass of vapor to the mass of liquid and it has a value obviously ranging from 0 to 1. So, x equal to 0 means a saturated liquid state x is equal to 1 means a saturated vapor state. Now, we can actually show that in general any property which is denoted by y, y average should be equal to the sum of y f plus x times y f g that is sum of the property of the saturated liquid plus quality multiplied by the difference in the property at saturated vapor and saturated liquid state. So, here y can take any value it could be either specific volume or it could be energy specific entropy or specific enthalpy. For example, we can write h average is equal to h f which is the enthalpy corresponding to the saturated liquid state plus the x which is basically the quality multiplied by h f g which is h g minus h f. So, most of the times we would drop this subscript average because it is known that we are just taking an average of the property.  And it is also known that the value of the property at liquid state that is h f or u f or s f should be less than or equal to the average value which will in turn be less than or equal to the value at the vapor state because at the vapor state it also has additional energy because of the latent heat. So, y f will be less than or equal to y average less than or equal to y g and so this is true for any of these properties whether it is specific volume or specific internal energy or entropy or enthalpy and so on. So, what we have seen is that for from a property table if you look at properties of steam for a particular pressure and temperature all these properties will be listed as different columns you would have h f h f g and h g similarly you would have properties for internal energy entropy and specific volume. So, from the table it is possible for us to determine these values rather than calculate them though it is possible to calculate them, but it can be quite complicated especially if you look at mixture of liquid and mixtures and so on. So, to keep thing simple especially when you are trying to solve problems property tables come in handy because based on the pressure and temperature one can determine all these properties corresponding to that particular pressure and temperature. Now, we have seen that on pressure temperature diagram as well as we have also shown the temperature and volume diagram. Let us look at the temperature and volume diagram of a pure substance again. Now, here we can see that on the left hand side of the saturated liquid line it is the compressed liquid state on the right hand side of the saturated vapor line is the super heated vapor state. So, let us look at some more properties of the super heated vapor state. So, all those properties which correspond to the right hand side of this vapor line saturated vapor line correspond to super heated vapor. So, region to the right of the vapor line and at temperatures above the critical temperature we have the super heated vapor region and in the super heated region which is basically a single phase region pressure and temperature are no longer dependent properties that is you can change pressure and temperature independent of each other unlike at other phases where they are basically dependent. So, compared to a saturated vapor a super heated vapor is characterized by the following that is if you compare super heated vapor and a saturated vapor super heated vapor is characterized by lower pressures that is p will be less than the saturated pressure pressure for a given temperature and temperature would be greater than saturated temperatures at a given pressure that is if you look at the pressures and temperature for a given temperature the pressure will be higher than that of the saturation pressure and if you look at the same pressure the temperature will be higher than that of the saturation temperature for super heated state and also in super heated state the specific volume enthalpy etcetera are higher than that at a given pressure or temperature that is for super heated steam for example, volume would be higher than that of the volume of the saturated vapor. Similarly, enthalpy of the super heated vapor will be greater than enthalpy of this saturated vapor internal energy of the super heated vapor is greater than the enthalpy of saturated vapor for a given pressure or temperature. So, these are some of the properties that are associated with super heated vapor similarly, we can also identify properties that are that correspond to that of sub cooled liquid which will be basically those lines those points which are on the left hand side of the saturated liquid line. So, that those all those points correspond to the compressed liquid state of the particular pure substance. Now, what we shall discuss next is on composition of a gas mixture that is if you were to look at mixture of different gases how do you analyze different properties of that particular mixture and like if you have to calculate enthalpy of the mixture how do you calculate them and. So, in order to do that we will define what are known as mass fractions and mole fractions of a particular mixture and then apply those for calculating different properties. So, let us consider a gas mixture which has let us say k components and let m subscript m be the mass of the mixture and n subscript m is the number of moles and therefore, m subscript m is equal to summation i is equal to 1 to k m i and n m is equal to summation i is equal to 1 to k n i. So, here let us also define mass fraction m f which is ratio of the mass of a component to the mass of the mixture and mole fraction y which is basically the ratio of the mole number of a component to the mole number of the mixture. So, m f i is equal to m i by m m that is mass of the component divided by mass of the mixture and mole fraction is mole number of the component to the mole number of the mixture. So, mass of a substance of mole number n and molar mass that of m will basically be equal to product of the two that is mole number multiplied by the molar mass and average mass that average molar mass and gas constant can also be calculated as m subscript m is equal to the mass of the mixture divided by the molar number of that particular mixture which is basically equal to sigma m i divided by n m which is sigma n i m i divided by n m and since n i by n m is equal to the mole fraction this is equal to sigma summation i is equal to 1 to k y i m i and therefore, the average gas constant for the mixture would be equal to universal gas constant divided by average molar mass of that particular mixture. So, which means that we can also now relate the mass and mole fractions of the mixture using this mole fraction sorry mass fraction which is m f i is equal to m i divided by the mass of the mixture which is finally, be equal to the mole fraction y i multiplied by m i by m m. So, the mass and mole fractions are basically related through the mass fraction m f i is equal to the mole fraction multiplied by the molar mass m i by m m. Now, so this is basically to calculate if you were to calculate different properties of a gas mixture if you can basically use some of these properties to identify and calculate average properties of a mixture of gases like average gas constant and so on and we shall also see how you can calculate average properties in terms of enthalpies and specific heats and so on. Now, ideal gas of we have also already discussed in two three lectures earlier about ideal gas equation and compressibility factor. So, ideal gas equation with a compressibility factor can be used for real gases this is something we have discussed earlier. So, prediction of the behavior of a gas mixtures can basically be whether it is real gas or ideal gas can be predicted by based on two laws one is known as the Dalton's law of additive pressures and the other is known as the Amagat law of additive volumes. So, Dalton's law of additive pressure probably you would have learnt this earlier is basically stating that the pressure of a gas mixture is equal to the sum of the pressures of each gas that if would exert if it existed alone at the mixture volume and temperature. Similarly, the Amagat's law of additive volume states that volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed alone at the mixture temperature and pressure. So, both these laws are can be used as it is for ideal gases, but these are kind of approximations for real gases that is these laws can be used in an approximate way for real gases one of the ways we could do that is by using the compressibility factor as well. Now, for ideal gases both these laws that is whether it is Dalton's law or the Amagat's law both of them give identical results whereas, it could be different it could be different results for real gases. So, let us look at the Amagat's and the Dalton's law. Dalton's law basically states that the mixture pressure is equal to summation i is equal to 1 to k p i which is the component pressure at the temperature and volume of the mixture. Amagat's law states that v m volume of the mixture is equal to summation i is equal to 1 to k v i at the mixture temperature and volume. So, both these equations are exact for ideal gases, but obviously they are only approximate for real gases. So, for ideal gases the component pressures and volume can be related to the mold fraction from the ideal gas equation that is p i we will use ideal gas equation for this p i that is component pressure at the temperature and volume t m v m divided by mixture pressure is equal to n i r u t m by v m which is for the component divided by n m r u t m by v m which is for the mixture. So, this reduces to n i by v n m that is y i that is the mold fraction. Similarly, we can also using the Amagat's law we can still write or equate that being equal to the mold fraction that is the ratio of the component pressure to the mixture pressure and component volume to the mixture volume is basically the mold fraction that is p i by p m is equal to v i by v m which is equal to number of mold ratio which is basically the mold fraction. So, this quantity which is product of y i times p m is called the partial pressure and the product y i by y i times the mixture volume is called the partial volume. For an ideal gas mixture all these that is the mold fraction the pressure fraction the volume fraction all of them are identical which is what I had mentioned here for an ideal gas this pressure ratio the pressure fraction the volume fraction mold fraction they are all basically the same. But they are not necessarily the same for real gases because if you were to use if you were to see a real gas because of real gas effects all these parameters need not necessarily be the same. So, let us look at real gases how do we apply Dalton's and Amagat's law for real gases what we could either do is use one of the advanced equations of states like Wanderweil's equation or the B.T. Bridgeman equation or so on or we could use the ideal gas equation itself with the compressibility factor. So, Dalton's law and Amagat's law can be used for real gases with approximations. So, either we use advanced equations which can be little complicated or we use the compressibility factor where P v is equal to Z n R U T where Z is the compressibility factor. So, Z compressibility factor for the mixture can be calculated if you know the compressibility factor for individual components. So, Z m is equal to summation i is equal to 1 to k y i Z i where y i is the mole fraction for each of the components. So, Z i can be determined either at T m and V m which is based on Dalton's law or at T m and P m which is based on the Amagat's law for individual gases. But again because these are not ideal gases if you determine it either is either of these ways they are not going to give you the same results. But what has been seen is that the Dalton's law seems to give more accurate results if you were to determine the compressibility factor at the mixture temperature and mixture volume. So, for gas mixtures if you are required to calculate extensive properties like energy, enthalpy, entropy and so on how do you calculate that? We can calculate them if you know the contribution of each of the individual components. For example, the internal energy enthalpy entropy can be expressed as of the mixture u m energy of the mixture is equal to summation i is equal to 1 to k u i which is equal to summation i is equal to 1 to k mi u i where mi is mass of individual component u i is in the energy associated with the individual component. Similarly, enthalpy and entropy can be expressed as summation of the products of the mass times the specific enthalpies and specific entropies of the individual components. Now, internal energy enthalpy entropy per unit mass can be basically determined by dividing the equations by the mass of the mixture that is u m that is specific internal energy of the mixture will be equal to summation i is equal to 1 to k mass fraction multiplied by the internal energy for each of the component. Similarly, enthalpy of the mixture will be equal to summation i is equal to 1 to k mass fraction multiplied by enthalpy of individual components and also for entropy, entropy of the mixture will be equal to summation i is equal to 1 to k m f i times s i where m f i is the mass fraction s i corresponds to entropy of individual components. We can also use similar properties for calculating the specific heat at constant volume and specific heat at constant pressure for the mixture that is c v m specific at constant volume for the mixture will be equal to summation i is equal to 1 to k m f i times c v i where c v i is the specific heat at constant volume for individual components. Similarly, c p m that is specific heat at constant pressure for the mixture will be equal to summation i is equal to 1 to k m f i times c p i. And so for gas mixtures, if you were to look at mixture comprising of several gas components, we can calculate the specific heats, we can calculate the internal energy enthalpy entropy etcetera for the mixture by summation of the mass fractions times the specific properties of the individual components that is mass fraction multiplied by let us say enthalpy of one component and sum it up for all of these individual components, we get the enthalpy of specific enthalpy of the whole mixture. We can also use the same properties for calculating the specific heats at constant pressure and constant volume for the mixture. Now, if you look at changes in these properties that is changes in enthalpy, changes in internal energy and entropy, we use the same principle that we have used for calculating the entropy enthalpy internal energy of the mixture itself. So, for calculating changes in internal energy enthalpy and entropy of a gas mixture during a process, we can calculate them as the following way delta u m which is the change in energy of the mixture is equal to sigma that is summation i is equal to 1 to k delta u i which is equal to summation i is equal to 1 to k m i delta u i. Similarly, delta h m is equal to summation i is equal to 1 to k m i delta h i and summation and for entropy delta s m is equal to summation i equal to 1 to k m i delta s i. So, that brings us to the end of this lecture, where we have been discussing about properties of pure substances. We have defined what is a pure substance, we have also defined what is meant by compressed liquid, saturated liquid, saturated vapor and superheated vapor. Basically, these are different states of water as they change phase from liquid to vapor. We have defined what is meant by saturation, temperature and pressure. We have different, we have discussed different ways of expressing these phase change processes in terms of property diagrams of pure diagrams, pure substances p v and p t diagrams and temperature volume diagrams. And property tables are those which basically help us in estimating many of these properties that is temperature and enthalpy, energy and so on. If we know the pressure and temperature of a particular process, then we have also looked at pressure p v t behavior of gas mixtures and ideal gas and real gas mixtures and properties associated with gas mixtures on how you can calculate the different properties like enthalpy and entropy and internal energy of a gas mixture, if we know the mass fraction of each of the components and the corresponding specific properties of that particular component. That is what we had, these are the topics we had discussed during this particular lecture. In the next lecture, what we shall be discussing are certain aspects which are quite different from what we have been discussing so far. We shall talk about one-dimensional compressible flows and we shall define what are known as stagnation properties and then we will define Mach number and the speed of sound and we shall take up analysis of one-dimensional isentropic flow. We shall understand the variation of fluid velocity with flow area and also look at isentropic flow through nozzles that is convergent nozzles as well as converging and diverging nozzles and so isentropic flow through these different types of nozzles is something we shall be discussing in next lecture as well as one-dimensional flow, compressible flow and properties of compressible flows is something that we shall be discussing in the next lecture which will be lecture number 22.