Physics 32 Kinetic Theory of a Gas (7 of 10) The Maxwell Boltzmann Distribution
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- เผยแพร่เมื่อ 19 ต.ค. 2024
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In this video I will explain the Maxwell Botzmann distribution and show you how to develop the most probable speed equation.
I am glad it helped. Thanks for the feedback.
Michel van Biezen thank you very much. You really made me understand it.
you're a life saver Mr. Van Biezen, I love you and I love your work!!
brilliant man. your videos helped me get A's in calculus based physics 1 and 2, and now they are going to help me get this A in physical chem as well. much appreciated!
I'm from India. And I'm in High school (11th grade), and My teacher taught us this in class but I consider this as a little complicated. But ur explanation makes it easy. And the orange bow looks so cute too
Finally someone coherent! Thank you so much for all your work and effort!
Very cool! You just combined/connected what I learned so far in my classes of math, chemistry and physics in a single problem! I really enjoy it! It’s so fun!
Glad you enjoyed it. Thanks for sharing. 🙂
Been trying to find a walk through for this for hours, this is the only explanation I have found and you explain it very well, thank you!
Becca M I feel you, literally hours. Hope college worked out for you haha
AYE you are a freaking life saver. Finally a GOOD PHYS CHEM TEACHER/PROF. SO MUCH BETTER!!!! Can actually comprehend.
Helped me ace Physics 2 and now a graduate course. YOU. ARE. THE. MAN!!
Great! Glad you found our videos helpful! 🙂
Michel, that was a fantastic presentation. Bravo! I am about to take over a position as an instructor, and I have found your videos to be the most valuable on Maxwell-Boltzmann. In our application, we will be looking at the speed of neutrons. I learned a lot from your intructor techniques, and especially like how you simplified the differention process by substituting in C2. I will try to modify your lecture and apply it to the classes that I teach to my students. Thank you again!
Rex. That is great! Good luck with your new position.
We all learn from one another. I had some very good instructors when I was in school and I always aspired to be like them when I had a chance to stand in front of a classroom.
I feel the need to thank you still. This video helped me tremendously. I don’t know what it was, but my brain was shattered when my professor skipped steps 1-all of them and came up with the final product. Sincerely, thank you!
Glad we were able to help
great explanation thank you for time taken. most difficult part to understand is why you choose second portion. it is little tricky but i got it. thank you
Never knew this 9yrs video would take care of my Test tomorrow ❤❤
Glad you found our videos. Good luck on your test tomorrow! 🙂
Hello sir It's Dushyant sharma and iam from INDIA . THIS IS THE BEST VIDEO EVER SEEN! Actually this topic comes in 11th grade in indian school but not the derivation ; due to my curiosity I watched this derivation and my all concepts are crystal clear. Thank you so much sir😘😘
Welcome to the channel! We are glad you found our videos. (There are more than 9500 of them). 🙂
It would be a pleasure be a student of your classes. Very neat and clear. My current physics teacher is very disappointing. Many classmates watch your lectures instead.
I was drowning on this topic until I found this video. Thank you so much.
Glad it was helpful!
To anyone interested in an easy derivation of this equation, we only need to make 2 (really 1) very simple assumption[s]:
1) A particle's energy in one direction doesn't influence the probability distribution of its energy in any other (perpendicular) direction. Put simply, P(E_x)P(E_y)P(E_z)=P(E_x+E_y+E_z)Or, even more simply, the velocity distribution is 'random'.
2) Probability distribution over speed (i.e., over kinetic energy) is continuous (precise speed measurement should correlate to a precise probability measurement). This really is just saying that our measurements need to make sense (probability measurement needs to be consistent, in the classical sense), so it's not an additional 'physics' assumption, really.
Combining (1) and (2) shows that the velocity distribution function has to have the e^{-v^2} form, and normalizing (setting total probability over all velocities equal to 1) gives the prefactor. Integrating over all velocities with the same energy yields the speed distribution, which is the equation on the board.
Michel, we would love to see your derivation of the MB distribution from the conservation laws.
Hello prof. first, your videos have been of great help for most of my engineering classes and for that I sincerely thank you! I'm having trouble understanding the proof of 'average Energy'= 3/2*K*T using the Maxwellian distribution and 'most probable Energy'=1/2*k*T also using Maxwellian distribution, if possible can you make a video. Thanks again.
You're awesome. When I first did the derivative I set one of my constants as C and didn't replace Cmp with V and got all my Cs mixed up.
I'm 16 y.o. and I got so confused when my teacher taught this in the class. U simplified it way better..Thank youuu:)))
wow ,what can say ,other than very neat and smooth .I have been struggling in understanding those concepts for a while not any more .thanks prof .
great video I kinda zoned out a little bit when you were doing the derivative. Watched it at twice the speed but I do that for all the videos to save time.
misssweethearted He used the product rule which is basically f'(x) = g'(x)*h(x) + g(x)*h'(x)
this guy is just too good
sir you are awesome
-California community college student
+dantesinfernoization What community college do you attend?
Thank you!
You are welcome. 🙂
Maxwell-Boltzmann satatistice
Do you have a video about it?
Just what you see in this playlist. We also have additional videos here: PHYSICS 32 KINETIC THEORY OF A GAS th-cam.com/video/GgiWD-MJicQ/w-d-xo.html
Fantastic video. Thank you.
thanks you you're the best
Excellent explanation. But isn't R the gas constant? In the video you said its Avogadro number. I have a doubt.
R is indeed the gas constant. (I may have misspoken).
@@MichelvanBiezen oh! I didnt expect that you'd respond to my comment. Thank you.
We try to repond to questions when time allows. You are welcome.
@@MichelvanBiezen thank you
Do you happen to know how to calculate the standard deviation of the molecular energy? I’ve looking for this all over the internet, I read a lot of books and nothing, can you help me please
We need something more specific than "molecular energy". However we know the curve of black body radiation (known as the blackbody radiation curve) and that curve represents the vibrational modes of the molecules of the walls of the blackbody. (The radiation curve of objects) So start with looking up the blackbody radiation curve. (and it is not a normal distribution curve)
@@MichelvanBiezen i was talking about maxwell-Boltzmanns energy distribution, the derivation of the energy
thank you usa you are my best friend
You are welcome. Glad you found our videos.
Great video, thank you.🙏🙏🙏
You are back at it. Keep it going.
Thank you for this explanation. This is Great!
Seven years later🥇
Thank you!!! Great explanation, easy to understand
Aweasome sir.....
Nice, simple n easy
This is Supraja ramachandruni that topic is easy to understand 😊
Where is the video of calculation of the rms velocity using maxwell distribution??
great man , thank you very much
You're welcome!
This made so much more sense than the book, thank you for posting such a helpful video. I really appreciate it :)
Sir is not to mind for exam.... but any thing also that to tips form physics
Thanks for the Help sir. Really appreciated.
wow It's the first time to understand that derivation
Glad you found the video helpful.
If, most probable velocity is the max value of the function how can it be Vrms>
Vmp? (Vrms = sqrt3RT/M, Vmp = sqrt2RT/M)
3 > 2 Not sure if we understood your question correctly. (Or are you asking WHY Vrms > V mp?)
@@MichelvanBiezen sorry professor, i got it wrong now i understand. (I thought Vmp and Vrms on the y-axis)
@@MichelvanBiezen you are the best thanks for the videos 👑
Super nice tutorial
Thank you
Loved it 😍
Thanks
sir plz can you give a brief lecture on degrees of freedom
I have added it to the list of topics to cover.
thankyou sir
hahahaha thats an actual topic? Its remarkable how 'they' can use irony and sardonicism and not be aware
much thanks!! really helpful lecture :)
Glad it was helpful!
Thank you so much!!
You're welcome!
Just awesome sir thank u
Great explanation! I just have one question: why does the higher temperature result in a “flatter and longer” graph? I understand that it’s because T is in the denominator of both fractions, but how exactly does that translate to a lower and longer graph? Thank you!
Assuming that the number of molecules is fixed, the vertical axis represents the number of molecules in the sample with a particular velocity. As you heat up the gas, the velocity of the molecules will increase and the number of different possible velocities will increase as well. Since there are now more velocities the molecules can have, there will be less molecules with the same velocity and the curve will be lower.
Michel van Biezen Oh right, that makes so much sense! Thank you!
where is the root mean square velocity of gas?????????:( :( I see both videos of average velocity and most probable velocity these are the only videos I was looking for, but video of mean square velocity is missing :(
It is in the playlist: Physics 32 Kinetic Theory of a Gas (6 of 10) Average, Mean, and Root Mean Square Velocity
I wanna see the derivation of f(v). Is it somewhere to be found?
Me too.
thannnnnnnnnnnnnnnnnnnnnnnnnnnnk you soooooooooooooooooooooooooooooooooooooooooooooooooooo much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
footpot,
Glad these are helping. Thanks for the feedback.
hahaha, helping no, that's an understatement your getting me through first year physics at university. Would it be possible to make videos on more complex and in depth physics (i.e deriving equations, particle physics, cosmology, further quantum mechanics and sticking to algebraic answers and to save time). thank you again
footpot
Yes, that is all in the plan, but it takes time to put out these videos. At this time there are some astronomy videos, that include some cosmology (the big bang theory) and I am planning a series on particle physics in the next several weeks.
Regarding your comment: "deriving equations", which equations were you thinking of?
Thanks
ALL of them, i'm not even joking. We expected to be able to derive every equation we use, so we not given an equation sheet. When ever you use a new equation, just spend the first video deriving it (even if its short). One equation that come to mind is snell's law, but any and every equations need to derived. Also don't be afraid to put more ads on the videos your content is good, students will still your videos watch.
if you want i can send you a list of topics covered by most first year courses, (this is the best group to target, as TH-cam is already saturated with high school physics videos)
sorry about the bad grammar its 3am here and i've been working since 1pm
footpot
OK Thanks. That gives me a good idea.
You better get some sleep. 3AM? What time zone are you in?
Excellent
Why do you use e instead 2 or other number ?
e is the natural number and appears in many natural processes.
Thanks sir
Sir , I have a question.
here , V(mp) is the maximum value of maxwell function f(v).
So, why v(mp) is smaller than v(rms) ?
....v(mp)/v(rms) = (2/3)^0.5 < 1
but why????
Please answer me Sir.
The vertical axis represents the probability that you will find a molecule with that velocity, (or it represents the number of molecules with that velocity in a volume). mp = most probable. It is more likely you will find a molecule with that velocity compared to finding a molecule with RMS velocity.
Sir could you make videos on uniform circular motion
Take a look at these: PHYSICS 11 ROTATIONAL MOTION
Thank you
sir f(E)=Ae^-E/kt can you plz tell about constant A
Greetings hope you are doing fine. I got a challenge on what exactly is the law of Maxwell-Boltzmann of diistribution for velocities of mokecules in a gas .
Assume you have a box with 1000 gas molecules. They would not all have the exact same velocity. Some would move a little faster and some would move a little slower than the average (or the most probable velocity). If you then plot each velocity of every molecule on a histogram, you would get the curve seen
+Michel van Biezen ok thanks you a lot sir,,and when we want to deduce the maxwell boltzaman law for the velocuties we will deduce all the velocities e.g vmps,averag velocitie ???
MAESTROOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!
Best Man !! :))
Thank you. Glad it was helpful. 🙂
Thankyou
You’re welcome 😊
Thank you so much
sorry sir plz help me,,, what are the significance of RMS,the mean and the most probable...
The mean is the same as the average. The RMS (root mean square) is the "effective" average, since the molecules with the greater velocities carry more "weight" in the averaging process. (That is the same as the "averaging" of the AC current and AC voltage. We use the RMS voltage and RMS current to find the "average" voltage and current. The most probable velocity is the velocity which has the most molecules traveling at that velocity.
thank uuuuu sir,,,,,,always am proud to listen your lecture and the way you answering me i was getting more concepts,,,💪💪💪
please give me any link to get Maxwell velocity distribution derivation
Are you referring to the Stephan - Boltzmann distribution derivation? We don't have a video on that yet.
@@MichelvanBiezen then sir please make the video
What is 'm' in the equation
Is that molar mass or mass of one molecules or mass of all the molecules
m = mass of 1 molecule and M = molar mass
@@MichelvanBiezen thanks
I need the derivation please ❤️
Thank u sir !
Nice
Thanks
Tq very much sir😊
Most probable mean most likely velocity
Why is there no dv? Is it only there when using dN/N????
Since f is a function of v, f' = df/dv (Like y if a function of x, so y' = dy/dx)
Michel van Biezen Oh you replied! Thank you so much! I have another question: can the most probable velocity be found using integration? Can vrms be derived using the method you showed in the video???
The standard method to find the most probable velocity is using differentiation, because you are looking for the point where the slope is zero (where the derivative is zero). Vrms is found using a different method.
Michel van Biezen ahhhh I get it now! thank you for answering all my questions, sir!☺
Explanation is amzing and awesome buttttttt the formula on the image of the video is wrong.
Which formula? And what is wrong with it?
Thank you!!!!
In my country we take the gas constant as R and not K 😂😂. Like there ths R=0.0821 almost everywhere in each and every book
With the MKS system of units, the correct value is R = 8.315 J/mol k But with non-standard units used in chemistry R = 0.08206 liter-atmosphere/mol K
Same here im also from india and this topic was not fully explained by the teacher so here i go on TH-cam and find great lectures by you dear sir
Thanks alot
Ha ha, profassor you are extra ordinary good❤️
Thank you! 😃
Boltzmann distribution of speeds
nice video but your standing in front of the equations so difficult to follow you, and you don't stand out of the way long enough for us to see the screen. Just a recommendation.
Yes, we are now shooting our videos differently to prevent that.
why we use v (rms) most of the time?
Statistical analysis shows that V rms gives us the correct total kinetic energy of the gas molecules. We have some videos on that topic in the playlist.
i love you
thannk!!!!!!!!!!!!!!!!!!!!!!!!!!!! u
Very bad
Maxwell's Boltzmann distribution ko define nahi Kiya or nahi ushka statistics ko bataya
Thank You!
You're welcome!
Thanks sir
Welcome