i know im asking randomly but does anyone know of a way to log back into an instagram account..? I stupidly forgot the login password. I love any tricks you can offer me.
Introduction and Course Overview 0:00 - Introduction to MIT OpenCourseWare and the Creative Commons license. 0:21 - Introduction to the course "8.333 Statistical Mechanics" and syllabus overview. Statistical Mechanics: Definition and Syllabus 0:37 - Rough definition of statistical mechanics. 0:45 - Detailed syllabus explanation. Course Structure and Content 1:00 - Equilibrium properties and thermodynamics. 1:51 - Introduction to probabilistic approaches in statistical mechanics. 2:32 - Central limit theorem and the law of large numbers. 3:11 - Degrees of freedom and perspectives in thermodynamics. 4:07 - Kinetic theory and its implications in statistical mechanics. 5:17 - Postulates and principles of equilibrium in statistical mechanics. Course Dynamics and Practical Information 8:49 - Information about the lecturer and teaching staff. 9:19 - Lecture and recitation schedules. 10:12 - Problem sets and their submission guidelines. 13:04 - Additional course materials and textbook recommendations. 15:03 - Grading system and integrity policy. 18:55 - Course outline and schedule flexibility. 19:50 - Anonymous question submission and responses. Introduction to Thermodynamics 22:58 - Introduction to the phenomenological description of equilibrium properties in microscopic systems. 24:19 - Background and relevance of thermodynamics in scientific study. 26:20 - Development of thermodynamics from a Newtonian perspective. 32:40 - The zeroth law of thermodynamics and its implications. 36:30 - Equilibrium conditions and empirical temperature. 42:24 - Ideal gas temperature scale and its derivation. First Law of Thermodynamics 56:20 - Explanation of the first law of thermodynamics. 57:38 - Idealized adiabatically isolated systems and work done on them. 1:03:10 - Diathermic walls and the definition of heat. 1:07:09 - Quasi-static processes and mechanical work. 1:12:43 - Displacements and generalized forces in thermodynamics. Heat Capacity and Joule's Experiment 1:17:24 - Heat capacity and its dependence on the path. 1:21:27 - Joule's experiment and its implications for the ideal gas. Conclusion and Preview for Next Lecture 1:25:49 - Summary of the lecture and a preview of the next topics.
As someone currently retaking this material at my own university, having been many years since last time, I still haven't found a better guidance through the Thermo laws with exactly the same level of math that my course requires. I love this. A true professor shows up in a suit and is covered in chalk dust by the end of lecture lol.
Dude provided the rough outline of the syllabus in such an artistic manner that feels like you have covered a long journey of the vast course in a short period of time
Needlessly to say, these series lectures are invaluable for people (like me) who are interested in statistical mechanics. Um.. personally speaking, such videoes can help me get a deeper insight into Kardar's books, which sometimes get confused so much. Before this, there were no complete, high-quality recorded courses on stat. mech (If you know, please tell me, and I will be appreciate it), it definitely fills a gap! Thanks a lot!! Looking forward to video courses on 8.334 statistical mechanics of field!!
It's uncut and somewhat difficult to follow on without some of the prerequisite knowledge. However, this is the best out there. (especially for free) It's nothing like ASAPScience or Minutephysics, but this gets the information out there with amazing demonstrations. I always learn better a follow-on video than reading some confusing Wikipedia article.
This first lecture is a bit abstract (not for absolute beginners) but you can learn a lot of things even if you have done some work on thermodynamics before watching this. Thank you.
If you had a tool to help you learn and be successful/pass thermo, what would you need in the tool? What issues/challenges did you experience taking thermo? What do you do when you are "stuck" and how do you get unstuck? If you have disabilities, what are accessibility needs to utilize an online tool? Why is thermo a difficult coarse?
Also we know that internal forces sum up to zero from newton's third law but not necessarily internal work... So if some dissipative internal forces are present inside the system then the work done will be path dependent
then that dissipated energy will remain inside the system , maybe pressure of the gas will increase, or something else will happen. But energy/heat will not come out from the system.
This professor’s lecture factors in his own (KPZ) equation, so the theoretical variances in his presentation bears a lot on the Kardar Parisi Zhang equations which may seem nontraditional/confusing to some.
Actually, at 41:28 when Professor Kardar says it'd be complicated to do rigourosly... it's not so much. We can use the implicit function theorem and thus get F (i.e. the function that solves for c1) in terms of the remaining variables (and of course, when substituted into f, it should also equal 0). The restriction is that we can only get a function that satisfies this property locally and as long as the derivative of f with respect to c1 is not 0. The conditions stated above are actually not satisfied when we have first order phase transitions (e.g. water to vapour). During these transitions we have constant temperature (which gives us the thermal equilibrium between systems) and the only properties we could determine with this theorem are Temperature and Pressure, since (for example) the boiling temperature of a liquid depends only on the Pressure (i.e. ∂T/∂P≠0, and of course the temperature itself). The above limitation implies that the other thermodynamic properties cannot be obtained from the equilibrium condition alone (in fact, it's customary to introduce the property of "quality" to deal with this situation). We can visualize this with the s-T graph (engineering-references.sbainvent.com/thermodynamics/t-s-diagrams.php#.Wo5Qf-FzLIU). We note here that T doesn't change during the phase transition (for constant P=Po, T=Ts) but this means that other properties that do change exhibit a discontinuity: If we have Ɛ arbitrarily small, (T,P)=(Ts-Ɛ,Po) corresponds to a liquid state, whereas (T,P)=(Ts+Ɛ,Po) corresponds to the gaseous state. We know that the gas has higher values for h, u, s, etc. than the liquid and thus we note that these properties are discontinuous with respect to T, this corresponds to the inapplicability of the implicit function theorem in this case. We can imagine this as turning the P=Po line 90 degrees (and rescaling to the appropriate values of the properties), then it's obvious that we have ourselves a discontinuity. Finally, it's worth noting that even when we don't have a continuous F for these particular values of T, we can use the theorem to conclude that for all T where we don't have these particular type of phase transition (this goes both for transition temperatures of system A and of system C... assuming we only have the solid-liquid and the liquid-gas ones (I frankly don't know if there are more of these or not) we would then have 4 (potentially) distinct T's) function F is locally continuous, and in general F would be piecewise continuous once we take the transitions into account.
Also, I forgot to mention that it doesn't matter if "solving for C1" resulted in a multivalued function. The implicit function theorem guarantees the single valued function that matches the original coordinates.
At 41:28, the word marked as "[INAUDIBLE]" in the subtitle text is probably "handwaving", in the sense how this term is used in mathematics (see the Wikipedia article "hand-vawing"). Thank You very much for the good and wonderful video!
The problem with this is contained in the word *equilibrium..* Which has the effect of tying the analysis to classical thermodynamics and avoiding or evading the true meaning of entropy, the macrostate and the Boltzmann equation which tells us how we know God exists and is the creator of the universe because nature is eliminated as a causal agent.
In the equation of heat which he wrote at 1:05:03 , ain't the first term and second term same, I mean, change in work is also equal to the difference between final energy and initial energy.
The first law of thermodynamics is that there can not be a zero temperature measured by human or mechanical but that does not mean either it exist or it does not zero because it has zero frequency meaning it has no dimension like consciousness Second law is that in an only in an isolated system can have work done but as a universal system zero sum is resulted meaning a whole universe can only transform but never had more or less in total energy or matter as a total sum Third law is that the entropy of the whole universe always increase meaning all would disintegrated into lighter material and consciousness will be a disconnected for rather than in solid line of metal or rock. Therefore quantum mechanic is a ultimate evolution not a avoidable state. Like before labor get salary future machine and energy help people get wealth by just thinking and brainstorming meaning jump in promotion is possible even without traditional educational training or licencing
54:45 would this represent a triple point for water? What about the pressure needed for the vapor to exist in equilibrium? Can anybody help me with this?
When he is explaining 1st law he first assumes that the system is adibatically isolated. And then he says, in the adiabatically isolated system if he goes from one equilibrium state to other, it is independent of path. But equilibrium is defined between the system abd surrounding. And system is already adiabatically isolated from surrounding. So which equilibrium is he talking about?
sir u made a slight mistake at 34:35 by saying that B and C are not connected to each other. But its okay. Its nothing to moan about. Thanx for the nice lecture
EL experimento de joules no es en un recinto aislado. It must be defined that it is an adiabatic isolation without involving the heat, otherwise it is a cyclic definition.
I don't understand how the gas expands from 1 tank into 2 tanks without changing in temperature. If the walls are adiabatic and the gas expands in volume, it must reduce in temperature kind of like when you let hairspray out of the can, the can gets cold. Can someone clarify why there was no temperature change?
Real gases behave exactly as you said, however you observe experimentally that the closest your gas is to ideal (very dilute) the less temperature change the gas experiences in the free expansion, hence you can say ideal gases don’t experience changes in temperature when they expand freely in adiabatic conditions. In short, experiments show that gases that are well described by the ideal gas model don’t change temperature when expanding freely and hairspray is not an ideal gas, hence it cools down.
One way of seeing it is that the constraint shouldn't depend on the derivatives of the co-ordinates(since it is an equilibrium). Also, it obviously isn't any inequality.
This is a graduate level class? I'm confused. I have to take "Statistical Mechanics" in my third year (undergraduate) first semester. Is this not the same type of class?
I had this class with Kardar back in '99. He's a brilliant professor. He never referred to notes while lecturing; he had it all in his head.
Me in '91. It is the same class. Never saw a question he did not address clearly & intelligently.
what job did you get with this knowladge
@@marsille0986good one
@@marsille0986a great job
@@marsille0986 one which pay well
Actual Lecture Starts at 22:30
That is really helpful (I truly mean it)
Thank you
Thank you. After about 10 minutes I was getting bored of hearing about the syllabus when I'm not truly enrolled in this class lol.
Utsav M
Ahh Thank you!!
Thank you 🙂
Great teacher. I'm 50 years old, never, i've seen a so clear course on thermodynamics. Lecture 4 is for me a jewel !
That's a greater lesson
He's iranian thats why. Us iranians are great at what we do
@@nazbah5929 You are just great at oil.
i know im asking randomly but does anyone know of a way to log back into an instagram account..?
I stupidly forgot the login password. I love any tricks you can offer me.
Now you are 56 years old
Introduction and Course Overview
0:00 - Introduction to MIT OpenCourseWare and the Creative Commons license.
0:21 - Introduction to the course "8.333 Statistical Mechanics" and syllabus overview.
Statistical Mechanics: Definition and Syllabus
0:37 - Rough definition of statistical mechanics.
0:45 - Detailed syllabus explanation.
Course Structure and Content
1:00 - Equilibrium properties and thermodynamics.
1:51 - Introduction to probabilistic approaches in statistical mechanics.
2:32 - Central limit theorem and the law of large numbers.
3:11 - Degrees of freedom and perspectives in thermodynamics.
4:07 - Kinetic theory and its implications in statistical mechanics.
5:17 - Postulates and principles of equilibrium in statistical mechanics.
Course Dynamics and Practical Information
8:49 - Information about the lecturer and teaching staff.
9:19 - Lecture and recitation schedules.
10:12 - Problem sets and their submission guidelines.
13:04 - Additional course materials and textbook recommendations.
15:03 - Grading system and integrity policy.
18:55 - Course outline and schedule flexibility.
19:50 - Anonymous question submission and responses.
Introduction to Thermodynamics
22:58 - Introduction to the phenomenological description of equilibrium properties in microscopic systems.
24:19 - Background and relevance of thermodynamics in scientific study.
26:20 - Development of thermodynamics from a Newtonian perspective.
32:40 - The zeroth law of thermodynamics and its implications.
36:30 - Equilibrium conditions and empirical temperature.
42:24 - Ideal gas temperature scale and its derivation.
First Law of Thermodynamics
56:20 - Explanation of the first law of thermodynamics.
57:38 - Idealized adiabatically isolated systems and work done on them.
1:03:10 - Diathermic walls and the definition of heat.
1:07:09 - Quasi-static processes and mechanical work.
1:12:43 - Displacements and generalized forces in thermodynamics.
Heat Capacity and Joule's Experiment
1:17:24 - Heat capacity and its dependence on the path.
1:21:27 - Joule's experiment and its implications for the ideal gas.
Conclusion and Preview for Next Lecture
1:25:49 - Summary of the lecture and a preview of the next topics.
Great
As someone currently retaking this material at my own university, having been many years since last time, I still haven't found a better guidance through the Thermo laws with exactly the same level of math that my course requires. I love this. A true professor shows up in a suit and is covered in chalk dust by the end of lecture lol.
lecture start at 23:16
pradeep singh thank you very much bro
Jio pradeep bhaai....Thank you so much for saving data and time
Bhai aaplog jee KE liye dekhe ho n ye video
You are gem, Pradeep!
I am proud that an Iranian professor teaches at this top university
I took this course as an undergrad 50 years ago, and all the talk of tests and problem sets, etc., still makes me break into a cold sweat.
Dude provided the rough outline of the syllabus in such an artistic manner that feels like you have covered a long journey of the vast course in a short period of time
Watching this lecture and listening to this professor, I wish I was 21 and still in school. What a great lecturer.
Thank you MIT. Such a good initiative to allow lectures from such renowned Professors from a renowned university to be freely available to everyone.
باعث افتخارم هست که ی استاد ایرانی به این خوبی درس ترمودینامیک را تدریس میکند.❤❤
منم همینطور ❤❤❤❤
Needlessly to say, these series lectures are invaluable for people (like me) who are interested in statistical mechanics. Um.. personally speaking, such videoes can help me get a deeper insight into Kardar's books, which sometimes get confused so much. Before this, there were no complete, high-quality recorded courses on stat. mech (If you know, please tell me, and I will be appreciate it), it definitely fills a gap! Thanks a lot!!
Looking forward to video courses on 8.334 statistical mechanics of field!!
It's uncut and somewhat difficult to follow on without some of the prerequisite knowledge. However, this is the best out there. (especially for free) It's nothing like ASAPScience or Minutephysics, but this gets the information out there with amazing demonstrations. I always learn better a follow-on video than reading some confusing Wikipedia article.
THANK YOU MIT. I got bored one day I found this subject and I’m interested in it. I can finally learn more about it
Thanks MIT OCW for giving me such precious Christmas gift...Thanks a lot again...
I agree. What a beautiful Christmas gift it is !! Finally, a set of video lectures on statistical mechanics is available online.
From Turkey at GAUN, thank you so much MIT
nice initative by mit to share knowledge and helps lot of student get quality content..!!
This first lecture is a bit abstract (not for absolute beginners) but you can learn a lot of things even if you have done some work on thermodynamics before watching this. Thank you.
i have no words to say thanks...
love from india
Looks like he was fighting the equilibrium position of that blackboard
😂😂😂😂😂
This teacher is insanely good.
Terrific teacher. Thank you for posting this, MIT.
Very impressive watching him seemly write phenomenological in cursive without stopping. If I were to lecture, that woulda been 3 min all but itself.
superb teacher, if not one of the best so far in this field!!! thx aloot
Thermodynamics is a phenomenological description of equilibrium properties of macroscopic systems. 23:50
This man is also an accomplished calligrapher!
One of the best lecturers to learn these things from.
literally this is the kind of content I´m watching at the end of the semester
If you had a tool to help you learn and be successful/pass thermo, what would you need in the tool? What issues/challenges did you experience taking thermo? What do you do when you are "stuck" and how do you get unstuck? If you have disabilities, what are accessibility needs to utilize an online tool? Why is thermo a difficult coarse?
Time to Practice, Practice , Practice. The 80-20 rule. Each round of practice you will fail 20% of the time.
Also we know that internal forces sum up to zero from newton's third law but not necessarily internal work... So if some dissipative internal forces are present inside the system then the work done will be path dependent
then that dissipated energy will remain inside the system , maybe pressure of the gas will increase, or something else will happen. But energy/heat will not come out from the system.
This professor’s lecture factors in his own (KPZ) equation, so the theoretical variances in his presentation bears a lot on the Kardar Parisi Zhang equations which may seem nontraditional/confusing to some.
Actually, at 41:28 when Professor Kardar says it'd be complicated to do rigourosly... it's not so much. We can use the implicit function theorem and thus get F (i.e. the function that solves for c1) in terms of the remaining variables (and of course, when substituted into f, it should also equal 0). The restriction is that we can only get a function that satisfies this property locally and as long as the derivative of f with respect to c1 is not 0.
The conditions stated above are actually not satisfied when we have first order phase transitions (e.g. water to vapour). During these transitions we have constant temperature (which gives us the thermal equilibrium between systems) and the only properties we could determine with this theorem are Temperature and Pressure, since (for example) the boiling temperature of a liquid depends only on the Pressure (i.e. ∂T/∂P≠0, and of course the temperature itself).
The above limitation implies that the other thermodynamic properties cannot be obtained from the equilibrium condition alone (in fact, it's customary to introduce the property of "quality" to deal with this situation).
We can visualize this with the s-T graph (engineering-references.sbainvent.com/thermodynamics/t-s-diagrams.php#.Wo5Qf-FzLIU). We note here that T doesn't change during the phase transition (for constant P=Po, T=Ts) but this means that other properties that do change exhibit a discontinuity:
If we have Ɛ arbitrarily small, (T,P)=(Ts-Ɛ,Po) corresponds to a liquid state, whereas (T,P)=(Ts+Ɛ,Po) corresponds to the gaseous state.
We know that the gas has higher values for h, u, s, etc. than the liquid and thus we note that these properties are discontinuous with respect to T, this corresponds to the inapplicability of the implicit function theorem in this case.
We can imagine this as turning the P=Po line 90 degrees (and rescaling to the appropriate values of the properties), then it's obvious that we have ourselves a discontinuity.
Finally, it's worth noting that even when we don't have a continuous F for these particular values of T, we can use the theorem to conclude that for all T where we don't have these particular type of phase transition (this goes both for transition temperatures of system A and of system C... assuming we only have the solid-liquid and the liquid-gas ones (I frankly don't know if there are more of these or not) we would then have 4 (potentially) distinct T's) function F is locally continuous, and in general F would be piecewise continuous once we take the transitions into account.
Also, I forgot to mention that it doesn't matter if "solving for C1" resulted in a multivalued function. The implicit function theorem guarantees the single valued function that matches the original coordinates.
Thank you MIT ! From S.Korea....
Hii I am Maharashtrain here and I just completed my 12th class and I started neet exam prep 2023
this lecture is very important, this is the basic of basic
At 41:28, the word marked as "[INAUDIBLE]" in the subtitle text is probably "handwaving", in the sense how this term is used in mathematics (see the Wikipedia article "hand-vawing").
Thank You very much for the good and wonderful video!
Thanks for your note! The caption has been updated.
@@mitocw Thank You very much for Your kind reply, and also thank You very much for Your work. I am very glad for the video.
Wow, this guy's hands are good. Straight lines, good penmanship.
This is my second watching. Even better the second time. ❤
Thank you for teaching me more about statistical mechanics.
Great lecture! Very clear and precise
Lecture starts at 25:10 skipping all comments and syllabus material :)
It would be nice if the camera focused on what was on the blackboard and not always on the professor.
Lion of statistical mechanics.
starts at 23:07
Thanks man
Não tenho esse nível de matemática, mas é lindo demais ver isso.
thank you MIT it's helpful resource for my studing
I like this video because it was very good.
!Great Lecture
Thank you MIT
Thank you Professor Kardar.
《粒子的统计力学（共26讲）》
ruclips.net/p/PLUl4u3cNGP60gl3fdUTKRrt5t_GPx2sRg
00:00 课程安排
== 第一章 热力学 ==
23:03 导论
32:40 第零定律
56:14 第一定律
非常酷的感谢
LOL, the way the blackboard keeps going up at 28:30
What a wonderful lecture!
Lisa, in this house we obey the laws of thermodynamics!
The problem with this is contained in the word *equilibrium..* Which has the effect of tying the analysis to classical thermodynamics and avoiding or evading the true meaning of entropy, the macrostate and the Boltzmann equation which tells us how we know God exists and is the creator of the universe because nature is eliminated as a causal agent.
About the subtitles. I think the person in the audience said "holonomy" at minute 38:51 .
Possible inspired from the expression "holonomic constraint" usual in Analytical Mechanics.
I think he meant polynomial
36:08 Legend
Big respect to the professor
dat dude iz great! also sounds like the cool old librarian type npc that gives you quests in the dessert portion of the game map
0:31 1:10:49
Easy and fun to learn 🤩
The Cv and Cv is reallly easy to calculate. but the all have the valours in the final tables
The Carnot equation and engine
lecture starts in 23:00 minutes.
In the equation of heat which he wrote at 1:05:03 , ain't the first term and second term same, I mean, change in work is also equal to the difference between final energy and initial energy.
Miny Minions change in work is equal to change in kinetic energy and here the energy can also be of potential or other form. Not just kinetic
blow air onto a heat sink, is thermodynamics through and through.
[What resources the professor introduces for study
I appriciate my country and my countrie's scientisis (Iranian scientists)
این رفیقمون آمریکاست
The first law of thermodynamics is that there can not be a zero temperature measured by human or mechanical but that does not mean either it exist or it does not zero because it has zero frequency meaning it has no dimension like consciousness
Second law is that in an only in an isolated system can have work done but as a universal system zero sum is resulted meaning a whole universe can only transform but never had more or less in total energy or matter as a total sum
Third law is that the entropy of the whole universe always increase meaning all would disintegrated into lighter material and consciousness will be a disconnected for rather than in solid line of metal or rock. Therefore quantum mechanic is a ultimate evolution not a avoidable state. Like before labor get salary future machine and energy help people get wealth by just thinking and brainstorming meaning jump in promotion is possible even without traditional educational training or licencing
Why does the blackboard keep going up on its own? It kind of ticks my OCD.
Blimey - this sort of nonsense sends my brain completely around the bend .
So he is mehran kardar
What are the preferred, best teaching textbook for today's physics and engineering Theromodynamcis course?
54:45 would this represent a triple point for water? What about the pressure needed for the vapor to exist in equilibrium? Can anybody help me with this?
Questions those asked by students are not audible.
Nice one
When he is explaining 1st law he first assumes that the system is adibatically isolated. And then he says, in the adiabatically isolated system if he goes from one equilibrium state to other, it is independent of path. But equilibrium is defined between the system abd surrounding. And system is already adiabatically isolated from surrounding. So which equilibrium is he talking about?
Equilibrium is defined by certain macroscopic variables not changing over time, not in relation to its environment.
that’s a highschool lesson in my country
Isn't AI contrary to laws of thermodynamics? Partially?
Brilliant!
thanks
sir u made a slight mistake at 34:35 by saying that B and C are not connected to each other. But its okay. Its nothing to moan about.
Thanx for the nice lecture
First 23 min of bla bla bla in a good class. Short introduction of 5 min was enough.
is lecture useful for meachnical engineering...if not than which TD lectures of mit
He is cleaning chalkboard with dry sponge... I think you should not do It, because you release chalk dust into the air, thus not clean air
That chalkboard just will not stay down
Starts @ 23:00 the first 23 minutes are admin and waffle, nothing to do with thermodynamics
Man. No grading on a curve?..brutal.
When I make fart, the heat travels forward. So really. Farts are an example of thermodynamics
thank u so much
Whoever recorded this needs to understand we don’t want to see the professor, we want to see the damn board
nah man i am down bad for the professor ngl 🥵
I took this course. It was at a different university though.
good lecture
EL experimento de joules no es en un recinto aislado. It must be defined that it is an adiabatic isolation without involving the heat, otherwise it is a cyclic definition.
Me from India❤️,and preparing for JEE
Can anyone explain me is this thermodynamics course related to Chemical Engineering or it is a course related to physics?
This is a physics course. See the course materials on MIT OpenCourseWare for more info at: ocw.mit.edu/8-333F13. Best wishes on your studies!
why am i here i have 2 tests in 4 and 8 hours about electronics and programming
Gracias.❤️
I don't understand how the gas expands from 1 tank into 2 tanks without changing in temperature. If the walls are adiabatic and the gas expands in volume, it must reduce in temperature kind of like when you let hairspray out of the can, the can gets cold. Can someone clarify why there was no temperature change?
Real gases behave exactly as you said, however you observe experimentally that the closest your gas is to ideal (very dilute) the less temperature change the gas experiences in the free expansion, hence you can say ideal gases don’t experience changes in temperature when they expand freely in adiabatic conditions. In short, experiments show that gases that are well described by the ideal gas model don’t change temperature when expanding freely and hairspray is not an ideal gas, hence it cools down.
This motivated me to read the book instead, no way I’ll sit through this asspain
Why does equilibrium imply holonomic constraints?????
One way of seeing it is that the constraint shouldn't depend on the derivatives of the co-ordinates(since it is an equilibrium). Also, it obviously isn't any inequality.
This is a graduate level class? I'm confused. I have to take "Statistical Mechanics" in my third year (undergraduate) first semester. Is this not the same type of class?
Yes, this course is a graduate level class.
CrushOfSiel Classes on the same topic can have varying levels of depth and requisite background knowledge.
"Because I don't really how to handle this concept of heat".