AULA: Como Termodinâmica será cobrado na Petrobras? - Parte 1 | ENG. PETRÓLEO

Added: 2026-05-19

[00:00:00]A few years ago, a dream began. A dream born from the desire to transform the lives of those seeking more than just a job. I've been on the same side as you. I've been unemployed, I've been undervalued, and I've worked in places where insecurity and uncertainty about the future were constant companions.

[00:00:16]IBGE estimates that nearly 15.5 million Brazilian graduates are outside the job market. In one year, this number increased by 13%. The crisis in the job market has hit young people hard. Newly graduated professionals are struggling to find a job in their desired field.

[00:00:35]And then when I graduated from college, you know, I managed to finish college on time and I thought, like, man, now I can work, I can stop being supported by my mother. The job market was pretty much a mess; I even managed to get an internship to finish my degree, but finding a job was impossible.

[00:00:57]Everyone was either firing people or at least not hiring, right? I know what it's like to fight to achieve something better, something that truly brings stability and security. Imagine working in your field of study, earning a salary of over R$10,000 per month, and never having to look for a job again in your life. This was the change that happened to me, and I truly wish it would happen to you. A fresh start with stability, security, and the opportunity to grow in a solid career. Our journey began in 2017, and we quickly realized the impact we were making. Over 60% of those who passed the Navy entrance exam were our students. Back in 2019 we already had over 5,000 active students, and in 2023 we surpassed the mark of 1,000 approved students. A special mention goes to the Petrobras, CNU, Air Force, Army, and many other competitive exams. The success we've achieved so far is just the beginning. What I want, what we want, is to see you achieving great victories in whatever public career you desire. For candidate number 1, preparation goes beyond just studying. We create high- quality preparation materials specifically tailored to each competitive exam. We also offer all the necessary support for you to achieve your goal. And the goal is clear: you not only secure a position, but you have a successful and stable career for the rest of your life.

[00:02:26]Join us. The transformation begins here with your decision to not stop until you reach your goal.

[00:02:32]And I managed to pass the English course at Cebras.

[00:02:36]But what would you do? Would you talk about us?

[00:02:38]Dude, I highly recommend Cero, you have a mentoring process there, a leader who will guide you, and you know you won't be walking alone. This gives you very important emotional support. You know where to find the information and what to do to get approved, right? It's different. Oh, it's on YouTube, everything's on YouTube, man. You can learn how to do heart surgery on YouTube, you can learn everything there. It's just that, you need a step-by-step guide, and that's already been pretty thoroughly explained in the course, you know? So, there's no need to think that you have to look at the course as an investment, right?

[00:03:14]Short, medium, long term, depending on your preparation, whether you're making mistakes or not. And to invest in that, being sure, as you said, right? You'll only fail if you have a health problem or if you give up in a desperate situation. And that approval changes everything, it really does. The guy goes, his son goes to a better school, he'll enroll him in a language course, he'll have the best health insurance. Uh-huh.

[00:03:36]And the certainty that every month changes there, that's also a very good thing to hear, right? A professional who's 40 years old, man, has never been late, I've never had any trouble with him. If we extracted a lot, we extracted a little, we were never late. It drips there every month. All my booze.

[00:03:51]So this is quite an achievement.

[00:03:54]Thanks too, right William? Because you guys were the pioneers there back in 2015. That little seed was planted, you know, it was watered, it grew and grew. I continued investing, I believed in the project, and, wow, thanks to you guys, this approval was a very important step forward. Thanks to you, Lauro, and the whole team at the old Marine Engineering Center, now Comiro 01. I'd get home, have dinner there, then breakfast, obviously, and then go study, you know?

[00:04:24]Obviously, the main tool for all of this was the course I took, which was the Concurseiro 01 course. It helped me a lot because it has many practice questions and many mock exams. I don't know if it's the right methodology, but it works for me, which is basically just doing exercises, reading a lot of theory, I read what I see I'm getting wrong a lot, and you correct it based on the feedback from the questions there. That's it. I don't know if it's the best methodology. I think if you look at the courses they offer, they always have theory followed by exercises. But I did it this way, mainly because of the short amount of time.

[00:04:59]It looks like it's not going to work. I've always thought that to pass a competitive exam you needed to prepare in what way? For years, focused only on that competition, right? No, it's possible in four months. The platform there helped me a lot with doing exercises. That's when I saw that theory, which wasn't very, very good. That's how I watched the classes, the video lessons. After studying and taking practice tests, I was doing really well. I was, I don't know, out of 120, I was getting around 105 right. Dude, I'm saying that a job competition isn't something immediate; it takes time for the results to come. It won't be on the first try, nor the second, but you have to study hard to get there. And the time will come. You don't need to be the smartest person in the world, or the best, but it 's about persistence, studying, and using the right tools, right? The classes and practice tests I had at Concurseiros 01.

[00:05:51]That helps a lot, right? It's doable and worth it, right, man? It is worth it. And it's worth it.

[00:05:56]I'll say that the key difference was the correct setup of the study cycle, the table of topics that will be covered, right? How many questions per subject have you had in recent years, and also, as I always mention, the practice tests, for those who like soccer, right?

[00:06:11]We don't do friendly tests with the national team, the guy puts on A, puts on B, puts on C, the simulated test is for the real test. Oh, I'm doing badly, man. So, try it, change the way you study, change the way you're taking the test. It's the opportunity you have to make a mistake. If we hadn't actually done the practice test on the day of the actual exam, we wouldn't have succeeded. So, that's the rocky road ahead.

[00:06:36]So when I got to the announcement, I was like, "Okay, it's possible to get there, but how am I going to prepare?" I didn't know where to begin.

[00:06:45]And if you don't have support, if you don't have someone helping you structure your schedule, understanding the exam guidelines, it becomes very difficult, much more difficult than understanding what you have to study, it's about what you can choose not to study, you know? To understand what you might not study, you have to understand how the exam board works, how the board asks questions.

[00:07:04]So, this focus on teaching materials has undoubtedly greatly increased my productivity. I recommend 100% how you guys did this for me, it helped me to do this curation. So, we're still before the official announcement, but you can already get yourself ready, get your house in order, and soon you'll be able to compete. You'll already be way ahead of the rest of the country who haven't done it.

[00:07:26]And I went looking for some support, some help, you know? And that's where I met the number one test-taker, right? And it was a blessing for me, because you were offering so many great things that would make my studies easier, right?

[00:07:40]I got the job, I worked in the Navy, and we used the preparatory course for competitive exams for the first time; I wasn't even a competitive exam candidate at the time.

[00:07:48]After that, we spent some time in the Navy, and I managed to pass the Petrobras entrance exam in 2022. And whenever people ask for recommendations, I always mention Concurseiro 01 (the number one candidate), and some of my colleagues are even watching the live stream right now. And every week someone sees my testimonial and sends it to me, saying: "You can trust Concurseiro 01, he'll prepare you well. Just have faith, just study."

[00:08:11]For those who don't know where to start, having that security, having a schedule there, which I remember you already provide a suggested schedule for. Having a mentor, that was also very interesting, right? Having a mentor who was already at Petrobras, who gave us tips on what might be on the exam, who also had a lot of study experience, and having the possibility of having a group there, to exchange experiences, ask questions. Wow, that gives me a lot of comfort when studying. So, I highly recommend it.

[00:08:48]Hello everyone, good evening to our petroleum engineering class. How are you all doing? Give me your feedback if you can hear my audio well, everyone.

[00:09:01]Good evening everyone. Waiting for your feedback.

[00:09:17]Good evening, Maria.

[00:09:22]Maria can hear us well. Hey everyone, welcome to our petroleum engineering live stream.

[00:09:39]Today, as we're doing for our petroleum engineering class, we're always dividing the material into two parts each month.

[00:09:50]The first part will cover the theory, the key points, the most important formulas we need to know. The second part will be problem-solving.

[00:10:03]Thermodynamics is very important for you petroleum engineering students, okay everyone? We've seen in past CES Gran Rio exams that around two or three questions on this very broad and extensive topic tend to be asked, usually either more practical or involving some theory. We 'd allocate about 50% to each of these approaches, okay? So, without further ado, let's begin. I know the content might get a little tedious, okay everyone? It's more focused on theory, so we can address our... Okay, just a few questions, okay?

[00:10:49]But it's good for us to remember, to know what will be most important in the exam, okay?

[00:10:56]So stay wide awake, pay close attention to our class, because it will be fundamental, okay?

[00:11:03]So, anything, any questions, just call us here and we'll answer you right away, okay?

[00:11:13]So, everyone, we're talking about thermodynamics here. Part one will be our theory and part two will be related to typical CES Gran Rio questions on this topic, okay?

[00:11:26]So, the first thing we're going to define, to understand the rest of the content, is what heat is.

[00:11:34]Heat, or caloric energy, is characterized by the transfer of energy that always occurs from a body with a higher temperature to another with a lower temperature. This is important. I've seen this tested in theoretical questions. Typically, heat propagation can occur in three ways: conduction, convection, and radiation.

[00:12:07]Conduction always requires a physical medium, a contact, right? Convection generally requires... There's an interface there to allow for this heat transmission. And radiation doesn't need a material medium to propagate, as is the case, for example, with the heat energy that reaches us from the sun, right? So, these are the typical ways we have this heat propagation.

[00:12:36]In the International System of Units, it's important to define which unit will govern this heat, this quantity of heat, okay? So, heat is measured in joules in the International System. But there's another unit that's also very characteristic for heat, folks, which is the cal or calorie. It's important to highlight this because sometimes the exam will give us this information in calories, right? And we'll have to do the conversion there. So we know that in the International System the unit is the Joule, but we also know that traditionally it can be the calorie.

[00:13:21]Food packaging, gym treadmills, and countless other applications give us a measure of heat in calories, right? So, it's important to remember that one calorie is approximately 4,184 J. Some exam boards give the relationship and others don't, okay? So, one calorie can also mean approximately 4.2 Jules there so you can do this calculation. Don't forget this relationship, everyone. It's very important.

[00:13:58]Once we know what heat is and its unit of measurement, we need to study a phenomenon that is frequently tested on the CESGran Rio exam. Then, mathematically, we'll also see what heat exchanges are, right?

[00:14:16]Temperature and final temperature after a certain heat exchange, right? What is the thermal capacity of an element, and so on. These are typical elements of this heat exchange.

[00:14:29]So, bodies that have different temperatures will inherently always exchange heat with each other. As we saw, the heat flow always occurs from the hot body, which is the one with the higher temperature, to the colder body, which is the one with the lower temperature. The heat flow will always follow this dynamic.

[00:14:55]A very important point that we will discuss is that in energy exchanges or heat exchanges, there will always occur, they can occur There are two types of changes: either temperature or physical state. For each of these changes, we will have a different quantity or specificity of heat. For example, if I'm going to perform a heat exchange and my water heats up, I only have temperature, so I have a certain amount of heat. But if I supply even more heat, then this heat is to heat it up, to change the temperature, but it may also be that I supplied so much heat that it exceeds 100ºC and it changes its physical state, right, from liquid to vapor. So now I have a quantity of heat associated with the temperature increase and another with the physical state. So it's important to make a separation, that these are different quantities of heat, one associated with temperature and the other associated with changes in physical state, right? So be very careful about this, because we will see later that there will be different formulas, okay?

[00:16:19]So, the first thing we will measure is to calculate this amount of heat needed when I only have changes in temperature. This phenomenon where I supply heat and I I only have changes in terms of temperature, folks, we call it the quantity of sensible heat, right?

[00:16:42]This quantity of sensible heat is designated by the letter Q, right?

[00:16:49]Given in the unit of the International System, which is the Joule. It is calculated as the mass, right, in kilograms of that body there. C is called specific heat, it depends on the material. Each type of material has a certain specific heat, and Δt is my temperature variation, the final temperature minus the initial temperature, that is, the temperature I was at before the heat transfer and the temperature I am at after my heat transfer. Right? We have to be careful with the units of measurement, because we have to observe, especially when we are going to practice the unit of this element here, our specific heat, because depending on the unit it is in, we repeat the units for mass and for temperature variation, because we will be able to cancel them. But that's a topic for when we're doing problems. But for now, pay attention to this expression that is associated with temperature changes and the units of measurement of heat. Specific. When we practice, we'll talk about this again, okay? So, we have this value for the amount of heat, which is called sensible heat. Another variable we can have, which is not yet associated with the issue of changes in the physical state of matter, is what we call thermal capacity.

[00:18:29]Thermal capacity is nothing more than the amount of energy needed to raise that particular element to that specific maximum temperature by 1°C. So, thermal capacity, given in capital C, is nothing more than mass times specific heat. So, pay attention. It may be that the specific heat is given in the question as thermal capacity. So, know how to differentiate here, because in this expression, MC is nothing more than the thermal capacity itself, which is capital C.

[00:19:13]So, pay attention to what is being given.

[00:19:18]Up to this point, we've seen the amount of heat associated with temperature changes; now we also have to learn how to calculate the amount of heat associated with changes in physical state, which, as I mentioned, are distinct moments. And different.

[00:19:38]When I only have a temperature change, I'll calculate it that way, right? MC del T. But when I also have, in addition to the temperature increase, a change in physical state, then we will also calculate, given the change in physical state, with the other expression, of course, associated only with the change in physical state, which is what we call latent heat, right? The calculation of the amount of heat involved in this change of physical state. And that's why it's important that we always remember and read, right, both the expression and carefully reading the statement to know what happened in those changes of state. We will then find out if there was a change of physical state.

[00:20:29]So, we will have to use the following expression: the amount of heat needed here to carry out the change of my physical state is given by my mass and also by L, where L is called latent heat, it depends on the material, the change of state from one phase to another, and also the temperature.

[00:20:52]So, note that it does not depend on the temperature, folks. Why does it not depend on the temperature? Because during the change of state Physically, matter will remain at that same temperature until it completely changes its state. That's why it's simply mass times our latent heat.

[00:21:18]So far, everyone, is everything alright? Is everyone okay? Give me your feedback, everyone. Is everything alright? Did you remember this expression? Didn't you remember this expression?

[00:21:50]So, everyone, did you remember the expression? Did n't you remember? Have you already studied the thermodynamics part?

[00:22:10]Perfect, everyone. This part that we just remembered here always has many questions that Gran Rio has been asking you. So, our second part of the class, which is next week, always happening every 15 days, we will certainly have many questions associated with this, okay? Another important point when we talk about thermodynamics, everyone, is our study of temperatures, okay? So, making temperature conversions, scale changes is also very important. So, that's why now we're going to enter a new topic. We're going to talk about temperature, right?

[00:22:56]Temperature, which is a scalar quantity, nothing more. It's about representing, right, the amount of kinetic energy, whether from the movement or agitation of my molecules. It will then represent the thermal state of the body, whether it's hot or cold. Low temperature will indicate low kinetic energy; the molecules don't move with as much freedom, while at high temperatures the molecules have a greater degree of agitation, as I mentioned here.

[00:23:35]An important point when we talk about temperature is the concept of thermal equilibrium. You'll see this a lot in thermodynamics questions. The term thermal equilibrium. What does thermal equilibrium mean? It's when I place two or more bodies in a typically isolated environment, right? And they begin to exchange heat with each other until they reach the same temperature.

[00:24:01]So, whenever a question mentions thermal equilibrium, it means that at the end of that process, the temperature of both reached the same value. For example, in an adiabatic system that doesn't exchange heat with the external environment, if I place medium A and medium B at different temperatures, after a certain time, these two... In this context, they end up reaching the same temperature.

[00:24:31]Both A and B will reach the same value.

[00:24:34]So, pay attention. Every time the question uses the concept of thermal equilibrium, it means: after the heat exchange, the temperature of all the bodies will reach exactly the same temperature. Don't forget that, okay, everyone? We're going to do a lot of questions on this subject. Let's underline this in the International System of Units, right? The SI unit, which may seem strange, is not the degree Celsius, which we are so used to, right? The SI unit for temperature is Kelvin, everyone. Be very careful with that, okay? We have other units commonly used worldwide. The most common unit is the degree Celsius. We don't talk about temperatures in Kelvin. For the United States, which represents a minority in this sense, they use Fahrenheit, okay? But for the most part, we use degrees Celsius worldwide, but in the International System it's Kelvin, generally more for scientific purposes, right? Just a reminder, and We'll see that right after this.

[00:25:46]When we talk about temperature, it 's always important to highlight some notable points. For the Celsius scale, we have two notable points, always using water as a base. We have 0ºC, which is the moment when water can be on the verge of solidifying or on the verge of becoming liquid, depending on where the process is going. And also the boiling point, which is 100ºC, when this water will stop being liquid and become vapor, or gas, if you prefer. So, for the Celsius scale, 0 and 100 are notable values.

[00:26:29]This scale has become very popular because it's very easy to remember, right? It's a centigrade scale, divided into 100 parts. And for water, which is our main reference, we have key values ​​to remember, right? Which are zero and also 100. 100. Zero for the melting point and 100 for the boiling point, okay?

[00:26:53]For the Fahrenheit scale and the Kelvin scale, it's also important, right?

[00:27:00]Especially in terms of questions, we also need to remember these notable points, okay? So, on the Kelvin scale, the notable points are the melting point in degrees Celsius, which is zero in Kelvin, is 273, and the boiling point in Celsius, which is 100 in the Kelvin scale, is 373.

[00:27:27]An important point of similarity here is that both the Celsius and Kelvin scales are what? They are centigrade scales separated into 100 parts.

[00:27:39]So, variations in Celsius are also reflected in variations in Kelvin. So, this is important. So, generally, I don't need to do conversions. That is, if the temperature variation is 5ºC, this is reflected exactly in a temperature variation of 5 Kelvin. Note that I did n't use 5º. Okay, just 5 Kelvin, right? So, temperatures are on different scales between Celsius and Kelvin, but the variations, since both are centigrade scales, are exactly the same. So no conversion is needed. An important point for us to save time during the test, okay?

[00:28:20]In the Fahrenheit scale, which is a bit more forgotten because generally only the United States uses it, we have that 0ºC, which is the melting point, is 32º Fahrenheit there, while the boiling point, which is 100ºC, will be 212º Fahrenheit here for us. It's not a centigrade scale. If we do the subtraction, it's a scale that is divided into 180 parts, right? So, both the fixed temperature and the variations require conversion, okay? But these values ​​here, which are key values, we always have to remember, okay, everyone? Don't forget this.

[00:29:07]It's very common, everyone, for us You have to convert either because the question specifically asks you to do a conversion, or because during the problem-solving process, in addition to what the question already asks for, it also requires that you make the necessary scale change, okay?

[00:29:28]So, if you want to memorize it, you can.

[00:29:31]If not, you can do the whole procedure that we are already used to doing with temperature changes, which is a simple rule of three, actually, based on our scales, right?

[00:29:44]But in terms of the formula, if I want to convert between Kelvin and Celsius and vice versa, I have that the temperature in Kelvin is the temperature in Celsius plus 273.15 or just 273, okay everyone? If we don't want to be so rigorous, okay?

[00:30:06]So, Kelvin is the temperature in Celsius + 273.

[00:30:11]And I can also, in this case, have the same relationship to convert from Celsius to Fahrenheit and vice versa as well, right?

[00:30:20]So I have that the temperature in Fahrenheit is 32 + 1.8 of the temperature in Celsius, Okay, folks. That's it, right? Just remember this to convert from one to the other and vice versa. So, it's important to highlight this, but it's possible that during the exam, I might not be working with either scale or another; in other words, the exam might give me a scale it invents. I can create a temperature scale. I can do that now, and I can even find relationships between the scale I invented here and others, like Celsius, Fahrenheit, Kelvin, or any other, okay? We just need to use a simple rule of three, right? And I'll even give you the typical expression we can use to do this.

[00:31:12]Let's imagine I have two linear scales, remembering that it has to be linear for this to be true, okay? These scales, one is scale X and the other is scale Y, right?

[00:31:27]How do I then obtain a relationship between these temperatures? It's a conversion law from one scale to another. It's very simple. Remember the notable points; in this case, for water, we... You 'll always need two notable points there. What do I do? So, my temperature on scale X, which is the variable I want to obtain, minus the temperature on scale X, first notable point, okay? divided by the variation TX2 at the second notable point - TX1. That is, if it were, for example, the Celsius scale, which would be water, TX1 would be 0, TX2 would be 100, for example, right? This is the same thing, but for another scale. In this case, I would have here Ty, right, which is typed wrong. Ty, men1, right, a reference temperature, for example, if it were Fahrenheit, it would be 32 divided by the subtraction of two notable points of that scale Y. If it were Fahrenheit, for example, it would be 32, which was the melting point, and 212, which would be the boiling point. I can do this with any scale.

[00:32:49]I just need to always have two notable points, and it doesn't necessarily have to be the melting and boiling temperatures. It can be any two points, okay? If you If you do this for any scale, you'll get a relationship between them there anyway, in any way, okay?

[00:33:12]So yes, this is essential both with regard to a question that will only require temperature or also a question that... They want you to convert first and then actually create the account there.

[00:33:31]Regarding the temperature, everyone, is everything alright? Do you have any questions?

[00:33:41]We can move on, everyone.

[00:34:14]Beauty? So, we saw heat transfer, which will decrease significantly, we saw temperature variations that can decrease either in one issue or within the scope of another issue to address another aspect there, okay? And another point we can address is thermal expansion, which we might eventually have a question about, okay?

[00:34:43]Thermal expansion, then, is simply the increase in the size of our body as a function of temperature variation, right?

[00:34:52]Or a decrease also due to temperature variation, right? So, typically, if I gain thermal energy, I then have an expansion, and if I decrease my temperature, I can have a contraction there, right?

[00:35:10]Our alterations in the dimensions of matter, including the expansion of fluids themselves, occur due to intermolecular forces, right? The more activity there is, the more space I tend to occupy, right? So they tend to move away, and I then have an increase in some dimension, or in more than one dimension, of my matter.

[00:35:36]Typically, depending on the shape and type of material, I can have alterations that are linear, that is, in only one dimension, superficial, typically in two dimensions, or volumetric. For example, if I have a thinner bar, it would be something more linear. If I have a modification on a circuit board, it would be superficial. If I have a sphere, it would be a dilation with more volumetric characteristics, right? It all depends on the initial measurement, shape, temperature variation, and coefficient of expansion so that we can then evaluate it. But the question always makes it clear to us what type of dilation is happening there, right?

[00:36:25]The first one we can talk about, which is usually the most common, is linear thermal expansion. I can then calculate this expansion, which I call L, which is nothing more than the change in length between the initial length, right, sorry, final length, at a final temperature, minus the initial length before undergoing any change in temperature state. So this "del L," the unit is obviously the meter, right? That's the unit in the International System.

[00:37:03]This expansion, therefore, depends on the initial length and the coefficient of expansion. We must pay attention to the unit of measurement, which must match both the length and the temperature variation. This coefficient of expansion is typically provided; it will depend on the type of material we use and Δt, which is the temperature variation. So this expression is also important, like others we've already covered throughout today's lesson; it's another expression you need to remember. Del L equals initial length times alpha times the temperature variation.

[00:37:46]As for surface thermal expansion, folks, it has a very similar formula. So now I'm going to have changes on the surface, that is, in the area, right? Since I would have two dimensions, right? So we have that the change in my area, that is, m², is nothing more than the initial area, the coefficient of surface expansion, and the change in temperature.

[00:38:13]It's important to point out that here I have another coefficient, which is the superficial one. If the problem tells me that I have a solid, but gives me the coefficient of linear expansion, an important relationship that is valid for some materials is that the coefficient of surface expansion is twice the coefficient of linear expansion. Just a reminder that this is for some materials, typically solids, okay? The expression is very similar, except now we're talking about something related to the area. And finally, we can have volumetric expansion, where the volume, the change in volume in cubic meters, is nothing more than the initial volume in cubic meters. Here I have gamma as the coefficient of volumetric thermal expansion and delta t as our temperature variation.

[00:39:14]If the volumetric expansion coefficient isn't provided there, but I have a solid, right? So I can state that this volumetric expansion coefficient is three times the linear expansion coefficient, right?

[00:39:33]So I have these three forms of dilation that can occur and that may be requested of us during the exam.

[00:39:42]I believe this part is fine, okay? But if you have any questions, just give us a call.

[00:39:47]I know that's a lot of content, okay everyone?

[00:39:50]We have a lot to talk about here, right? That's because thermodynamics is a very broad subject to cover in just over an hour, but we're covering the main points, okay? One topic in thermodynamics that is frequently tested is ideal gases. So, when we talk about the practical aspects, what we've studied so far tends to be very relevant. But when we talk about the theoretical part, folks, this subject about the characteristics of ideal gases, or even the first and second laws of thermodynamics, also tends to be tested a lot, okay? So, let's talk about these characteristics or the study of ideal gases, right?

[00:40:40]Ideal gases are composed exclusively of point-like particles.

[00:40:50]So, we already have a first characteristic of ideal gases: they have particles of negligible size that are in chaotic motion at very high speeds.

[00:41:04]In an ideal gas, the temperature and the translational speed of the particles are proportional.

[00:41:13]Since there is no interaction between the particles of an ideal gas, the internal energy is always equal to the sum of the kinetic energy of all the particles that constitute it.

[00:41:30]So, some important points, some characteristics of ideal gases that we should always remember, are that in ideal gases the particles have negligible dimensions. Even the gases that would actually be real there exhibit behavior very typical of ideal gases. Another characteristic of ideal gases is that they have variable volume.

[00:41:58]This gas, considered ideal, will take the shape of its container. So, as we can see in our figure, the volume of an ideal gas is variable, always adapting to the shape of the container, right? Since these particles are always in constant, chaotic motion at high speed, they are constantly expanding, occupying the entire volume of that container.

[00:42:30]Another characteristic is that its shape is variable, that is, depending on the container it is in, it assumes the shape of that container, unlike solids or liquids, which do not adapt to the shape of the container. No, the gas adapts to that shape.

[00:42:59]So, depending on the shape of the container, I'll have a different shape for my gas.

[00:43:07]An important characteristic of ideal gases is their high compressibility.

[00:43:17]Because the particles that make up gases have very high kinetic energy, they are always very far apart from each other, making them easy to compress. In other words, I can bring them closer together, as we can see in the figure below where I have a flask with a plunger, right? Then I can compress this gas of mine here.

[00:43:40]And another point is that it has great potential for expansion. So, as we've seen, it tends to expand throughout the entire container.

[00:43:51]Other characteristic points of ideal gases, right, that we can talk about is their temperature, right? The higher the temperature, the greater the kinetic energy.

[00:44:03]Therefore, there is consequently greater expansion of this gas, and vice versa. in relation to its density. Ideal gases typically have very low density, as we know, and as we've seen in other lessons about fluids, density is simply the ratio of mass to volume.

[00:44:24]As we saw with gases, they have a very large expansion, the particles typically become very far apart, and they already have a very small mass. So it has a very small mass and a very large volume. So, that's why the densities of our gases are typically so low, right?

[00:44:52]Now that we've seen what can be considered an ideal gas and what the typical characteristics of these ideal gases are, everyone, we need to go to the mathematical part to refresh your memory.

[00:45:06]So, through the studies of three great scholars, we developed the laws associated with ideal gases, combining them with one of the most important, which is the ideal gas equation. Let's assume, then, that I have gas, right? And he's going to be subjected to two distinct phases, okay? It will have two conditions, an initial condition, an initial thermodynamic condition, where it will have a certain pressure P1, a temperature T1, and a volume V1. And after some effect on it, it will have another final state, where I will have a pressure P2, a temperature T2, and a volume V2. In other words, it underwent some kind of transformation there to go from an initial point to a final point.

[00:46:06]The general gas law tells me, then, that these variables will relate in the following way: the product of pressure and volume divided by temperature in the initial condition must be equal to the product of pressure and volume divided by temperature in the final condition, right? Don't forget, there are some changes to this law depending on the conditions of the gas, but in general it remains true, which is the ideal gas law. P x V over T is equal to P x V/ T.

[00:46:45]But now in the second moment, right?

[00:46:48]So, this general gas law tells us that the product of pressure and volume divided by temperature— remembering that this temperature must be in SI units, which is Kelvin— is a constant, in fact, that between the initial and final moments, this product and this division by the temperature does not change, right? And this constant, right, that is generated between these moments there, we give it a nice name, right, which is called the Clapeiron constant.

[00:47:21]So, we have that P x V in that gas, at that moment, pressure times volume, right, equals N x R x T. We studied this a lot in high school and it's back to haunt us here in the Petrobras exam, but we're going to do well. So I have to consider this constant there, right, the product of pressure and volume divided by temperature; that's always a constant. So I have that P x V (pressure times volume) equals N, which is the number of moles. R, which is a universal gas constant, okay? I provide here a value of 0.082 or more as 8.314 SI units times the temperature, which is given in Kelvin. Therefore, PV = NRT, the Cperon constant, and above that is the ideal gas equation. It's important for us to remember that. But this ideal gas equation, folks, it can be simplified depending on what I need there, okay? If my gaseous transformation occurs under certain conditions, and typically we separate three conditions there. We can then have this gas transformation occurring at a constant temperature, or it can occur at constant pressure, or at a constant volume. In each of these cases, I have a simplification of the use of the equation or the general gas law, right?

[00:49:00]When I have an isothermal transformation, as the name itself suggests, it means that I go from one state to another while maintaining a constant temperature, while pressure and volume change, but the temperature remains exactly the same throughout the entire process. If I then apply this concept that the temperature is constant, my general gas law equation ends up being just this simplification. When I have isothermal changes or transformations, the initial P x V is equal to P x V, right? It's good to remember these names. Isothermal means the same temperature, right? I can also have isobaric transformations, which are a little harder to remember, which is when I have changes in my gas, but with the pressure remaining constant, meaning the temperature and volume changed, but throughout the entire process the pressure remained exactly the same, right?

[00:50:09]When this happens, I call it an isobaric transformation. And my general gas law there, it can be simplified as initial volume divided by initial temperature equals final volume divided by final temperature, which is therefore an isobaric transformation.

[00:50:32]And I can have yet another type, or last typical type, of transformation, which is my isovolumetric transformation, also known as isochoric transformation.

[00:50:45]Isochoric or isovolumetric transformation, you can find both names there. This occurs when I experience changes in pressure and temperature, but throughout the entire process, the volume remains constant. When this happens, then, in the isochoric transformation, my general gas law ends up being reduced to P1 over T1, that is, pressure over temperature at the initial moment is equal to pressure over temperature at the final moment, right? And finally, a transformation that does not involve changes in pressure, gases, or volume. It's one more thing for us to understand our language there, which is the adiabatic transformation.

[00:51:35]Let's be literal here in this case.

[00:51:38]Therefore, we have that adiabatic transformations are thermodynamic processes in which no heat transfer occurs between the system and its surroundings.

[00:51:50]Generally, all those transformations, or transformations involving ideal gases, are adiabatic, because it implies that the transformation occurred without losses, right?

[00:52:03]The only possible energy exchanges during the adiabatic process result from the performance of thermodynamic work.

[00:52:13]In atiabatic transformations there is no heat exchange, that is, there is no heat loss. I can transform heat into motion or other forms of energy, such as work, but during this exchange, during this process, I don't lose heat, right?

[00:52:30]So, it's basically like a lossless system. So, in that sense, when we have this process, what does the first law of thermodynamics tell us? The change in internal energy of a gas during an adiabatic process, that is, without losses, is equal to the work done by the gas. This is simply a consequence of the law of conservation of energy. He's saying that if I remove or add internal energy to this gas, that's exactly the same as the work I did on it or the work I removed from it, right? For example, steam engines, right? It is a type of heat engine that uses the expansion of gas to perform work. In other words, if we consider an ideal adiabatic process, with no heat loss, all the heat I supplied to that gas represented an increase in internal energy, which was subsequently converted into work, and that's exactly what this law is telling me. All the internal energy of the gas ends up being converted into work, right? In fact, displacement in that direction, okay? So, write this down: the first law of thermodynamics tells us this when I have the atbatic transformations there, okay? This is a very important point for us.

[00:53:58]And if we want to present our first law of thermodynamics in the most complete version possible, it says the following: both work and heat cannot be measured or calculated for a single thermodynamic state, right? These quantities only have meaning when measured at different times. In other words, the first law of thermodynamics, when I don't consider adiabatic conditions, the most complete version of it will tell me that this amount of heat is nothing more than the work done plus the internal energy of the gas.

[00:54:44]When the first law of thermodynamics is applied to adiabatic processes, there is no heat loss, which is zero. That's why work equals the change in internal energy. But we know that's impossible, right? We always experience heat loss. For example, in air conditioning, right? We have work to do, you know, with the compressor and everything else. We have the internal energy of the gas there, but we also have heat loss to the environment. So, the complete general version of the first law of thermodynamics says that this heat lost, right, the heat received is the work plus the change in internal energy of my gas, right?

[00:55:28]As I mentioned earlier, the first law of thermodynamics is simply the law of conservation of energy. In other words, in a thermodynamic process, energy is conserved as internal energy is converted into both work and heat loss. It's the same little thing we studied back in the conservation of kinetic energy and potential energy. Here it's the same thing, only thinking in terms of thermal energy, right?

[00:56:04]Therefore, we can say that when my system receives heat, it can change its internal energy and also perform work. It can therefore involve altering internal energy, performing work, or one thing or another, without necessarily happening simultaneously, right?

[00:56:27]A typical example, right, of these three variables—heat, work, and change in internal energy—that we have there, for the first law of thermodynamics, is if we place a container with gas over a flame, what happens? I supply energy to this gas in the form of heat. What happens with that? The molecule becomes agitated, it expands.

[00:56:53]So, I increase the internal energy. And what else can happen if I expand this gas? I can try pushing the lid, right? So I can get work done too. So I have heat causing a change in internal energy and potentially also being able to do work, which is exactly what the first law of thermodynamics tells us, right?

[00:57:21]So, in the thermodynamic process, some of the heat that this gas receives can be converted into internal energy, and some can also be used to perform thermodynamic work, right?

[00:57:35]So, the sum of the two components, work and the increase in internal energy, is exactly equal to the heat that I supplied or eventually removed from that system, right? So, depending on what happens in this system, we can say that this work is positive or negative. If the volume increases, the work is positive.

[00:58:03]But if the volume decreases, we can consider the work done on the gas to be negative, right?

[00:58:12]In thermodynamics, to be able to visualize this thermodynamic work, it's very common to use graphs, right? So, in thermodynamics, work plays a very important role, because its purpose is to measure the construction of heat engines.

[00:58:34]That's why all these theories were developed during the first industrial revolution, right? Since that's where we ended up using heat engines the most at those times, like, for example, steam engines, right? In an attempt to increase their efficiency, these studies ended up being developed, right?

[00:58:56]Typically, thermodynamic work can be visualized through a graph, such as the one I 'm showing here, a graph of pressure versus volume. The area below our graph is simply the work. In other words, when I'm changing the pressure and volume of my gas from point A to point B, this work here, in this case, would be positive, right? Because I'm turning up the volume here. The area below gives me this task, right? And an important point is that if I have certain conditions, if the temperature doesn't change, I don't have a change in internal energy. If the temperature increases, I have an increase in internal energy. If the temperature decreases, I experience a reduction in my internal energy. So we can study the signs of that variable of mine, right?

[01:00:01]As we mentioned, the first law of thermodynamics, which we've been discussing for some time now, is simply the principle of conservation of energy, but applied to thermodynamic systems, right?

[01:00:16]The whole principle of conservation of energy, which seems a bit clichéd, but is one of the most beautiful things in the universe, is that no energy is created, much less destroyed, only transformed indefinitely all the time, right?

[01:00:33]As we can see in this figure, when I supply heat, in this case to any piston, I increase the energy of that gas and consequently I can also perform work, which is basically the graphical representation, right, illustrative of the first law of thermodynamics so that you can better understand.

[01:01:02]Once we have studied the first law of thermodynamics, it is important to highlight the occurrence of some cyclic transformations, which is a particular case of occurrence, right? A gas transformation is classified as cyclic when the initial state of the system coincides with the final state.

[01:01:28]For example, in the pressure and volume graph, as shown below, the initial and final points are exactly the same, right? And we learned that the area under the graph of a pressure-volume graph is nothing more than the work itself, right?

[01:01:48]So, the difference, right, the work done to complete that entire cycle is the area of ​​this cyclical region here that we're seeing. So, as I said before, calculating my area under the curve gives me the numerical value of the work done throughout the cycle of going from the end to the beginning, right?

[01:02:13]Typically, if my cycle occurs in a clockwise direction, I have what I call a motor cycle, and the work is positive.

[01:02:23]If this cycle occurs in a counterclockwise direction, as shown here, the work done is negative.

[01:02:32]This is what I've been calling the refrigerator cycle, right? It's important to highlight that our thermal machines end up revealing a lot about this subject here. And another topic that has been coming up a lot for us, folks, in the exam, especially this one from Petrobras, since we work a lot with systems involving this type of element, is thermal machines.

[01:03:01]But before we move on to that, and remembering that I know it's a lot to take in, how are we all doing, everyone? Is everyone able to remember and grasp the most important points?

[01:03:14]Are you writing down what's most important to you? How are we doing over there, folks? Tell me about it. We have quite a few students in our live stream today about petroleum.

[01:03:52]In that case, Maria, it's not the work involved in thermodynamics that's different, right?

[01:03:56]It's not zero in this case, because notice that for me, from point A to point B I follow a different path than from point B to point A. If the path were exactly the same, the work would be zero, but since I take different paths, I end up having a difference in pressure and volume. And consequently in that area, which indicates that work has been done, right? That's because we don't follow exactly the same route to go and to come back, okay? It's not that it's different. The principle is always the same. In this case, it's simply because we're on different trajectories.

[01:04:54]Okay everyone, if we're not sure, let's move on to heat engines so we can see what's most important in this topic.

[01:05:03]So, speaking about heat engines, we have that heat engines are those capable of converting heat into work, operating in cycles, which is why the professor already mentioned cyclic transformations.

[01:05:21]And they will typically use two different temperature sources.

[01:05:27]That which we call a hot source, which generally provides that heat, okay? And we also have the cold source, right, which is where the rejected heat is directed. So let's remember these names, hot spring and cold spring. The hot source is the heat I receive in my system, while the cold source is the heat lost, the heat given off, right? It's a loss, is n't it? Regarding heat engines, it's always important to know that they never transform all the heat given off or received by the machine into work. There's no such thing as a machine with 100% perfect efficiency, okay? So I supply the heat to the machine. This machine does the work, but I have losses there, right? Which is what we call a cold spring.

[01:06:26]Therefore, I never achieve an ideal heat engine with 100% efficiency. Right? Here in the figure, it is very clear that there is an example of a heat engine, where I have the hot source, right, with a temperature value of T1 and heat Q1. It performs a job, but I reject part of it, you know, I lose some of that heat too, you know, in the machine's casing, to the environment, etc. There, which is my heat being given off or cold source, typically designated by the index 2, right, Q2, right, which is the quantity of heat, and T2, which is my temperature there, right?

[01:07:08]The efficiency of a machine, folks, the efficiency of a heat engine can always be calculated if we develop our expressions here, using the following formula: 1 minus the ratio between Q2, which is the temperature, sorry, which is the amount of heat from the cold source, divided by the amount of heat from the hot source, right? Therefore, the efficiency of a heat engine in general can be calculated as 1 - q2 over q1, cold source over hot source. So, instead of talking about machines in general, we can talk about a specific heat engine, the most famous of all, which is our Carnox cycle or Carnox machine, which is described by our Carnox cycle, okay? So, the Carnox cycle is nothing more than a circle, a particular cycle of thermodynamic transformation of a heat engine performed on an ideal gas, right? The Carnoe circle is composed of two isothermal transformations, as we are seeing here, that is, at the same temperature, one expansion and one compression, and two adiabatic transformations, that is, without heat loss to the environment, as we are seeing here, right? How does this cycle work, right?

[01:08:42]Divided into four parts, with two isothermal and two adiabatic.

[01:08:47]So, initially, this ideal gas undergoes an isothermal transformation. It's going to expand, right?

[01:08:55]So, if it expands, it has absorbed heat from a hot temperature source here, right? This is the point here, my isothermal expansion. After an isothermal transformation occurs, the gas undergoes an adiabatic transformation, meaning it does not lose heat to the surrounding environment. As it then expands adiabatically, the temperature drops to a value T2, as we are seeing here.

[01:09:27]Next, this gas undergoes isothermal compression and releases a certain amount of heat to the cold source.

[01:09:36]And finally, it returns to its initial condition after undergoing adiabatic compression, which is the explanation for each section of the Carnu cycle, as we are showing here. And that's where it comes in, to explain this cycle and the machine that will respond to this cycle here, which will tell us the following. Carno's theorem states that no machine operating between two heat reservoirs, T1 and T2, has a higher efficiency than a Carno's machine operating between those same reservoirs. In other words, the carnô machine is the machine that will deliver the highest possible yield, and no other machine will be able to surpass it, right?

[01:10:31]A meat processing machine is simply a machine that operates according to this cycle, right?

[01:10:37]In this case, to calculate the efficiency of a machine governed by the Carnox cycle, I simply need to use the expression that this efficiency is one minus the temperature. Note that the previous expression was the quantity of heat, right?

[01:10:53]Here, the temperature of the cold source is divided by the temperature of the hot source. So, 1 minus the temperature of the cold source divided by the temperature of the hot source. The map, or Carnosa cycle, to be more precise, comes up quite often in our exams, especially in the thermodynamics section. That's why we want to bring up a lot of issues along those lines for you, okay?

[01:11:25]Given all this, and noting that this is a very important matter for you all, okay everyone? Please write this down so you can reinforce your studies, and we're bringing this review to you. We can talk about the second law of thermodynamics, right? The second law of thermodynamics is simply about energy transfers. The principles of this law state that all heat is spontaneously transferred from the body with the higher temperature to the body with the lower temperature. We already saw that, right? And since every process has losses, the efficiency of any thermal process is always less than 100%.

[01:12:08]And this law will tell me, then, that this efficiency in general for any cycle can be calculated as QA - QB divided by QA, which is a version of that 1 - q2 over Q1, right, actually, if I do the LCM there, QA here for us is the heat supplied by heating and QB is the heat not transformed into work, right, that is being lost. So, QA would be the hot source for us, and QB would be the cold source for us here, okay? So, exactly that expression that we presented in a general way there, but here now written, right, in the form of the second law of thermodynamics. It's also important for us to write this down, everyone.

[01:13:02]Just so we don't forget, if you're one of our students and are buying a package, feel free to use my coupon code Arthur 50. You'll get a discount of R$ 50 on your purchase. It'll give you a snack for the evening, right? Depending on what you're going to eat, it'll help you out, okay?

[01:13:24]In terms of theory, that's what we were going to discuss with you all in this class. I know it's a lot. We 're studying thermodynamics in class, but I'm bringing up the most important aspects so that in two weeks we can start tackling our own questions and everything will make more sense to you, okay? Now is the time for you to ask any questions you may have about the exam, this subject, or any other topic you'd like to know about. Folks, I'm available to you now.

[01:14:28]Maria. The forecast, okay, that we're going to have. Of course we'll come back to this topic, but for now I'm going to give you a lesson on practice questions, okay? It's a very broad subject, I know that, but we're going to address the issues to make it clearer. If we feel the class needs it, we'll come back another time to do more thermodynamics lessons, okay?

[01:15:16]Class. So, if you have no doubt, homework is a big subject, it's not difficult, okay? But that's a lot. We saw the amount of heat, temperature, expansion in ideal gases, heat engines, the carbon cycle. There are several other types of cycles, but this one is more associated with the pump part, okay? That's why we didn't even bring it here, and we know it's a lot of stuff. So, in the next class, we're going to bring up some questions so you can relax, so you can see that some involve applying the formula and paying a little attention to units of measurement in some other things, and in others, focusing on the theory, but we 'll practice with you, okay? So there's nothing to worry about. And then we'll move on to part two, so we'll be doing these questions with you in exactly 15 days, okay?

[01:16:12]Guys, if we have no doubts, then we'll see each other very soon, okay? Do your homework, review this material, if you can, go over this lesson again, take the necessary notes so that in the next class we can bring up the questions and you will be more informed, right, and you can clear up any doubts you may have, okay? Have a great night, happy studying, and see you later, everyone.