Introduction 0:00 - Introduction and Creative Commons License Review and Thermodynamics Structure 0:20 - Review of previous lecture and the structure of thermodynamics Equilibrium in Thermodynamics 0:33 - Emphasis on equilibrium in thermodynamic studies Mechanical Coordinates 1:09 - Discussion of mechanical coordinates in thermodynamics Gases in Thermodynamics 2:07 - Focus on gases, especially ideal gases Temperature and the Zeroth Law 3:01 - Inadequacy of mechanical coordinates alone; introduction of temperature 3:38 - Explanation of the Zeroth Law of Thermodynamics Isotherms in Gases 5:09 - Isotherms in gases, especially dilute gases Internal Energy and System Changes 6:02 - Exploration of system changes and the concept of internal energy Joule's Experiment 8:28 - Joule's experiment and its implications Theoretical Constructs in Thermodynamics 11:28 - Theoretical construction of functions in thermodynamics Quasistatic Processes 13:12 - Quasistatic processes and their importance in accurate calculations Second Law of Thermodynamics and Entropy 15:21 - Introduction of the Second Law of Thermodynamics and entropy Historical Context of the Second Law 17:28 - Historical context and relevance of the Second Law Heat to Work Conversion 20:05 - Heat to work conversion in engines and refrigerators Kelvin and Clausius Formulations 23:05 - Kelvin and Clausius formulations of the Second Law Equivalence of Kelvin and Clausius Statements 27:15 - Logical equivalence of Kelvin and Clausius statements Carnot Engine 33:43 - Carnot Engine and its properties Carnot Cycle with Ideal Gas 39:18 - Description of Carnot cycle using ideal gas Adiabatic Paths in Carnot Cycle 47:19 - Mathematical description of adiabatic paths in the Carnot cycle Efficiency of Carnot Engines 49:00 - Efficiency of Carnot engines between two temperatures Proof of Carnot Engines' Efficiency 53:14 - Proof of Carnot engines' efficiency being the highest Thermodynamic Temperature Scale 57:42 - Introduction of the thermodynamic temperature scale Consistency of Temperature Scales 1:07:59 - Discussion on the consistency of temperature scales Recap and Energy Function in Thermodynamics 1:14:42 - Recap of the lecture and the energy function in thermodynamics Introduction to Clausius' Theorem 1:20:08 - Introduction to Clausius' Theorem and entropy quantification
There's a lemma used here that's left unproven at around the one hour mark. We need to show that chaining two Carnot engines is equivalent in efficiency to a single Carnot engine. It isn't really hard to prove using the optimization lemma and reversing one of the engines connected to T_2, but it's not trivial. Good to leave as an exercise to reader, though, haha.
I don't agree with your view that something was left unproven. At around 0:55 he already proved that all Carnot engines operating between the same pair of temperatures have the same efficiency. The two chained Carnot engines that he considers at around 1:00 when seen as a single combined engine obviously fulfill the general definition of a Carnot engine (definition at 0:34): 1. it is reversible, 2. it is cyclic and 3. it operates only between two reservoirs (T1 and T3). (The third reservoir T2 is irrelevant and can be taken out of the picture by putting Q2 coming out of sub engine 1 directly into sub engine 2.) Hence, the efficiency of the combined engine has to be the same as that of any Carnot engine operating between T1 and T3.
I thought the question at 15:20 was really interesting. I wonder if the answer is along the lines of "yes, but to get such a threshold, you would have to be doing nonequilibrium thermodynamics'
I mean, it does make sense to ask for a tolerance below which you can guarantee accuracy for a numerical derivative, right? I guess the analogy isn't perfect though.
It's calculus: d(3/2 P V) = 3/2 d(P V) = 3/2 (P dV + V dP) = 3/2 P dV + 3/2 V dP. The first step is constant multiple rule (for differentials), the second step is product rule and the third step is just multiplying out.
Wrt. the argument for the CE being the most efficient, is there any logical dependence on it being a CE? Like it seems that you can just substitute any refrigerator in there and you could derive a conclusion that u \ge \frac{1}{\omega}. The only thing that the CE seems to contribute is that it allows you to make direct inferences about its capacity as an engine from its capacity as a fridge.
In the proof at 50:00, How does he prove that the carnot engine is the most efficient engine without using any specific properties about the Carnot engine? Also if we assume an engine E which is more efficient than the carnot engine C, then shouldn't E be able drive the carnot engine and still have some left over work?
You dont need any specific properties of Carnot engine. You only need that it should be reversible and returns back to its initial state (i.e. is a cyclic process). This is because every Carnot engine no matter how it is constructed has the same efficiency between two temperatures. He proves that Carnot engine is the most efficient by reversing the engine into a refrigerator at 51:30
A Carnot engine means an engine working with two external heat sources (a cold one & a hot one) where the cycle is a sequence of adiabatic-isothermal-adiabatic-isothermal processes. It is not possible to construct a Carnot engine that behaves perfectly (that is why I mentioned adiabatic processes instead of isentropic processes) so they will never reach the Carnot efficiency limit. But some cool examples have been built, such as the one in ["Brownian Carnot engine", by Martinez et al, Nature Physics (2016) 67, 12 (1)] where the authors use an optically trapped Brownian particle as the "gas" (a gas of 1 particle).
Clausius says that the sole result of a process cannot be the transfer of heat from colder body to hotter body. The net process here is the intake of Qh'-Qh heat from the hot reservoir and then depositing Qc'-Qc heat at the cold reservoir. So according to Clausius, the heat must be flowing from hot reservoir to cold reservoir. So both Qh'-Qh and Qc'-Qc should be positive, because if it were negative it would imply that heat is flowing from cold reservoir to hot reservoir(which would violate Clausius). So Qh'-Qh is positive or Qh'>Qh. Also from the net process diagram, It must be that Qh'-Qh=Qc'-Qc so as to satisfy energy conservation.
We can show that this relation that you wrote , is proven by applying 2nd law of thermodynamics in Kelvin form for non-carnot and carnot engine separately. for non-carnot engine , according to 2nd law , we should have Q_h' > Q_c' because (efficiency of non-carnot engine) = W/Q_h' = (Q_h' - Q_c' )/Q_c' = 1 - Q_h'/Q_c' ; so in order that (efficiency of non-carnot engine) < 1 , we must have : Q_h' > Q_c' ; because carnot-engine is a reversible engine , we can say that it's efficiency doesn't change by reversing the process. Now because we have a similar way of conclusion for carnot engine as before for non-carnot engine , we can say this time : Q_h > Q_c for carnot engine. By subtracting the side-by-side of this inequality , we have : Q_h' - Q_h > Q_c' - Q_c ; according to clausius form of 2nd law , the Q_h' - Q_h must be positive.
In the postulate of Kelvin´s seconde principle it is necessary to indicate that the intermediate fluid perform a cyclic transformation. Before explaining the Carnot cycle, Carnot's theorem should be taught
Good luck. The essays were released two days ago. It's scary to think that we only have three months until our application is due! Where did time fly?!
I heard lecture 1, and It is awesome that his lecture's logic and connectivity is so great.... after I listened his explanation, I jizzez in my pants... ha.... so good...
I usually take all of my classes with MIT, this is the first time I am in such a huge disappointment at the lecture. He is so fast and I cannot catch him, and I do not know why is he going over these topics and mathematical procedures without further physical explanation, Please MIT take care of the idea you have international students who need you guys to be a little bit slower.
you can pause the video, there are lecture notes to supplement this video and you can look at the text by Huang ...this is MIT, one of the most prestigious schools in the world especially with respect to STEM, you can't expect them to slow down when they expect you to already know thermodynamics, especially when this is a graduate level class ...not to mention this is free
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
I feel so lucky that these lectures are free online.
It is not free you are paying for the data
Introduction
0:00 - Introduction and Creative Commons License
Review and Thermodynamics Structure
0:20 - Review of previous lecture and the structure of thermodynamics
Equilibrium in Thermodynamics
0:33 - Emphasis on equilibrium in thermodynamic studies
Mechanical Coordinates
1:09 - Discussion of mechanical coordinates in thermodynamics
Gases in Thermodynamics
2:07 - Focus on gases, especially ideal gases
Temperature and the Zeroth Law
3:01 - Inadequacy of mechanical coordinates alone; introduction of temperature
3:38 - Explanation of the Zeroth Law of Thermodynamics
Isotherms in Gases
5:09 - Isotherms in gases, especially dilute gases
Internal Energy and System Changes
6:02 - Exploration of system changes and the concept of internal energy
Joule's Experiment
8:28 - Joule's experiment and its implications
Theoretical Constructs in Thermodynamics
11:28 - Theoretical construction of functions in thermodynamics
Quasistatic Processes
13:12 - Quasistatic processes and their importance in accurate calculations
Second Law of Thermodynamics and Entropy
15:21 - Introduction of the Second Law of Thermodynamics and entropy
Historical Context of the Second Law
17:28 - Historical context and relevance of the Second Law
Heat to Work Conversion
20:05 - Heat to work conversion in engines and refrigerators
Kelvin and Clausius Formulations
23:05 - Kelvin and Clausius formulations of the Second Law
Equivalence of Kelvin and Clausius Statements
27:15 - Logical equivalence of Kelvin and Clausius statements
Carnot Engine
33:43 - Carnot Engine and its properties
Carnot Cycle with Ideal Gas
39:18 - Description of Carnot cycle using ideal gas
Adiabatic Paths in Carnot Cycle
47:19 - Mathematical description of adiabatic paths in the Carnot cycle
Efficiency of Carnot Engines
49:00 - Efficiency of Carnot engines between two temperatures
Proof of Carnot Engines' Efficiency
53:14 - Proof of Carnot engines' efficiency being the highest
Thermodynamic Temperature Scale
57:42 - Introduction of the thermodynamic temperature scale
Consistency of Temperature Scales
1:07:59 - Discussion on the consistency of temperature scales
Recap and Energy Function in Thermodynamics
1:14:42 - Recap of the lecture and the energy function in thermodynamics
Introduction to Clausius' Theorem
1:20:08 - Introduction to Clausius' Theorem and entropy quantification
is the professor a god??, i am utterly in awe at how fluently he delivers his lecture
Lecture effectively starts at 15:00
Starts 2nd Law at 15:00
The professor's son is in the class.... that's so damn awesome!
@1:06:51 for those who don't understand how
@@rupeshknn why not grandson? lol
@@窦泽华 yeah that's possible too XD
Poocha?
25:55 To the camera operator: we're here a decade later, still appreciating you and your tracking of these blackboards.
23:00 to 33:00 is great! Never understood this in other books.
#MIT2019 Can't wait to start! I'm so thankful I've been given this chance.
waiting for an update
Great lecture from the Iranian professor
At 54:00... I don't get the definition of efficiency for the CC. It should be output/input
There's a lemma used here that's left unproven at around the one hour mark. We need to show that chaining two Carnot engines is equivalent in efficiency to a single Carnot engine. It isn't really hard to prove using the optimization lemma and reversing one of the engines connected to T_2, but it's not trivial. Good to leave as an exercise to reader, though, haha.
Didn't he implicitly justify it when he showed that the efficiency is a function of the two temperatures?
I don't agree with your view that something was left unproven. At around 0:55 he already proved that all Carnot engines operating between the same pair of temperatures have the same efficiency. The two chained Carnot engines that he considers at around 1:00 when seen as a single combined engine obviously fulfill the general definition of a Carnot engine (definition at 0:34): 1. it is reversible, 2. it is cyclic and 3. it operates only between two reservoirs (T1 and T3). (The third reservoir T2 is irrelevant and can be taken out of the picture by putting Q2 coming out of sub engine 1 directly into sub engine 2.) Hence, the efficiency of the combined engine has to be the same as that of any Carnot engine operating between T1 and T3.
I thought the question at 15:20 was really interesting. I wonder if the answer is along the lines of "yes, but to get such a threshold, you would have to be doing nonequilibrium thermodynamics'
I mean, it does make sense to ask for a tolerance below which you can guarantee accuracy for a numerical derivative, right? I guess the analogy isn't perfect though.
I'm sure it's just some calculus/algebraic move but I can't understand the step exactly at 46:58. If anyone can help I'd really appreciate it!
It's calculus: d(3/2 P V) = 3/2 d(P V) = 3/2 (P dV + V dP) = 3/2 P dV + 3/2 V dP. The first step is constant multiple rule (for differentials), the second step is product rule and the third step is just multiplying out.
@@Waffleschmerz Thank you! The application of the product rule is what got me.
Wrt. the argument for the CE being the most efficient, is there any logical dependence on it being a CE? Like it seems that you can just substitute any refrigerator in there and you could derive a conclusion that
u \ge \frac{1}{\omega}. The only thing that the CE seems to contribute is that it allows you to make direct inferences about its capacity as an engine from its capacity as a fridge.
In the proof at 50:00, How does he prove that the carnot engine is the most efficient engine without using any specific properties about the Carnot engine? Also if we assume an engine E which is more efficient than the carnot engine C, then shouldn't E be able drive the carnot engine and still have some left over work?
You dont need any specific properties of Carnot engine. You only need that it should be reversible and returns back to its initial state (i.e. is a cyclic process). This is because every Carnot engine no matter how it is constructed has the same efficiency between two temperatures. He proves that Carnot engine is the most efficient by reversing the engine into a refrigerator at 51:30
Does the crosses lowercase 'd' have a specific meaning in 'dW' or 'dQ' (other than the usual differential) or is it just the script he uses for 'd'?
They indicate a path dependence - to determine a differential in work, a path in P-V space must be specified.
《粒子的统计力学（共26讲）》
ruclips.net/p/PLUl4u3cNGP60gl3fdUTKRrt5t_GPx2sRg
第一章 热力学
00:00 上堂课回顾
15:03 第二定律
33:39 卡诺机
Anybody knows an example of Carnot machine "made" with any different thing than a gas?
Carnot engine is imaginary..
A Carnot engine means an engine working with two external heat sources (a cold one & a hot one) where the cycle is a sequence of adiabatic-isothermal-adiabatic-isothermal processes. It is not possible to construct a Carnot engine that behaves perfectly (that is why I mentioned adiabatic processes instead of isentropic processes) so they will never reach the Carnot efficiency limit. But some cool examples have been built, such as the one in ["Brownian Carnot engine", by Martinez et al, Nature Physics (2016) 67, 12 (1)] where the authors use an optically trapped Brownian particle as the "gas" (a gas of 1 particle).
that board seriously need to chill it is defying laws of physics in a physics class
at 53:00, can someone explain how Q_h' > Q_h follows from Clausius? Wouldn't Clausius just say Q_h' - Q_h > Q_c' - Q_c ???
Clausius says that the sole result of a process cannot be the transfer of heat from colder body to hotter body. The net process here is the intake of Qh'-Qh heat from the hot reservoir and then depositing Qc'-Qc heat at the cold reservoir. So according to Clausius, the heat must be flowing from hot reservoir to cold reservoir. So both Qh'-Qh and Qc'-Qc should be positive, because if it were negative it would imply that heat is flowing from cold reservoir to hot reservoir(which would violate Clausius). So Qh'-Qh is positive or Qh'>Qh. Also from the net process diagram, It must be that Qh'-Qh=Qc'-Qc so as to satisfy energy conservation.
We can show that this relation that you wrote , is proven by applying 2nd law of thermodynamics in Kelvin form for non-carnot and carnot engine separately. for non-carnot engine , according to 2nd law , we should have Q_h' > Q_c' because (efficiency of non-carnot engine) = W/Q_h' = (Q_h' - Q_c' )/Q_c' = 1 - Q_h'/Q_c' ; so in order that (efficiency of non-carnot engine) < 1 , we must have : Q_h' > Q_c' ; because carnot-engine is a reversible engine , we can say that it's efficiency doesn't change by reversing the process. Now because we have a similar way of conclusion for carnot engine as before for non-carnot engine , we can say this time : Q_h > Q_c for carnot engine. By subtracting the side-by-side of this inequality , we have : Q_h' - Q_h > Q_c' - Q_c ; according to clausius form of 2nd law , the Q_h' - Q_h must be positive.
I’m always impressed with lecturers who don’t use notes👌😉 That’s extremely sexy in an intelligent way👍🏾 That’s impressive 👏
In the postulate of Kelvin´s seconde principle it is necessary to indicate that the
intermediate fluid perform a cyclic transformation.
Before explaining the Carnot cycle, Carnot's theorem should be taught
awesome course
Thank you.
I really do not understand why all of that is useful to know!
I wanna join MIT !
That makes two of us! Only two and a half more years! (and hopefully I get accepted!)
I really want those physics and math doctorate degrees! :D
:) gooood luck
wish me too XD
Good luck. The essays were released two days ago. It's scary to think that we only have three months until our application is due! Where did time fly?!
Yo. Did ya get in?
thank you
who is this professor?
Mehran Kardar. See the course on MIT OpenCourseWare for more info at: ocw.mit.edu/8-333F13. Best wishes on your studies!
@@mitocw @mit openCourseWare, your previous interface was much better, now there is no option to download course content as zip
Try Nptel lecture of thermodynamics of SK SOM
I heard lecture 1, and It is awesome that his lecture's logic and connectivity is so great.... after I listened his explanation, I jizzez in my pants... ha.... so good...
Gracias.
Thank you so much
He never used the phrase "no free lunch" and I'm not mad... I'm just disappointed.
Free-lunches do exist. But they are very hard to get. Ask Mr. Jarzynski.
Very good lecture.
We wazzzz Kangz
Pope Jean Mac
if you cant explain it to a 12
I hate Thermodynamics
It means, you don't know about thermodynamics
Nerds lol
I usually take all of my classes with MIT, this is the first time I am in such a huge disappointment at the lecture. He is so fast and I cannot catch him, and I do not know why is he going over these topics and mathematical procedures without further physical explanation, Please MIT take care of the idea you have international students who need you guys to be a little bit slower.
you can pause the video, there are lecture notes to supplement this video and you can look at the text by Huang ...this is MIT, one of the most prestigious schools in the world especially with respect to STEM, you can't expect them to slow down when they expect you to already know thermodynamics, especially when this is a graduate level class ...not to mention this is free
Learning at MIT is supposed to be like drinking from a fire hose! lol IHTFP
his accent makes it difficult to concentrate , no thanks