The Incorrect Assumptions of the Ideal Gas Model - and Why It Still Works!

What exactly IS an Ideal Gas? And why do physicists use this model to represent real gases? In this video we'll compare the assumptions made by the ideal gas model with the properties of real gases, as well as how we can improve the ideal gas law in certain scenarios.
As with every model in physics, the Ideal Gas model makes some assumptions. Firstly, it assumes that every ideal gas is made up of tiny perfectly spherical particles. This is not necessarily true for real gases - yes they're made up of tiny particles, but they're not spherical.
Secondly, the ideal gas model assumes the average distance between each particle is much, much bigger than the size of each particle. This is true for real gases at relatively low densities, but the assumption breaks down when the density increases.
Thirdly, the ideal gas models assumes there are no intermolecular forces between particles (apart from when they collide with each other). And, these collisions have to be perfectly elastic (i.e. no loss of total kinetic energy). Again, all of this is untrue for real gases. Many have intermolecular forces (though usually these are quite weak), and collisions aren't always elastic.
So why does the ideal gas model make these assumptions? Well, that's because even with these assumptions the model makes very close, reasonable predictions about the behaviors of a real gas. And these assumptions make the study of gases (especially the mathematics) much easier to deal with. Therefore, the closer a real gas is to behaving like the assumptions of the ideal gas model, the better the ideal gas model is for representing the real gas.
Additionally, in situations where the ideal gas assumptions break down, we can actually modify the ideal gas assumptions. For example, for gases with diatomic molecules (two-atom molecules), we can get rid of the "hard spherical particle" assumption, and instead replace each particle with identical diatoms. Then, we can account for the rotational kinetic energy stored by each diatom.
Also, for gases at higher densities (where the distance between particles is of the same order as the particle size, and the intermolecular forces are no longer very weak), we can replace the ideal gas law with the van der Waals gas equation.
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Timestamps:
0:00 - Why is an Ideal Gas known as an Ideal Gas? What's Ideal About It?
0:46 - Assumptions of the Ideal Gas Model: Hard Spherical Particles
2:19 - Average Intermolecular Distance is Greater Than Particle Size
3:18 - No Intermolecular Forces between Particles?!
4:10 - Here's Why The Ideal Gas Model Still Works!
6:08 - Improving the Ideal Gas Model - Diatoms and van der Waals Gas
7:36 - Thanks for Watching! Merch Linked Below :)

[@ParthGChannel]

Thanks for watching everyone! Aside from a video on the van der Waals gas equation, let me know what other topics you'd like me to cover in a video!

[@DuckStorms]

The Schwarzschield solution to Einstein’s field equations and in particular the Schwarzschield radius.

[@DuckStorms]

Bernoulli’s equation

[@DuckStorms]

Langrange multipliers

[@DuckStorms]

Bessels functions and string instruments.

[@DuckStorms]

The heat and wave equations

[@DuckStorms]

Yes definitely want to see a video explaining the van der wall corrections to the ideal gas law.

[@DuckStorms]

In particular it’s interesting that the pressure correction is proportional to the square of particle density. I wonder why that is.

[@rocketsandmore6505]

Yea its in my syllabus too pls make

[@BitwiseMobile]

Me: I'll consume any physics you have. Parth: Let me know if you want me to make a video on physics topic X. Me: YAAAS!

[@bhushanpatil9303]

Adding to it: Generalized compressibility charts are really helpful in selecting at what temperature and pressure we can treat the real gas as ideal gas.

[@rachna273]

kzbin.info/www/bejne/j5vIYWeppdSGsM0 kzbin.info/aero/PLWsIqGN0VSKlEA2d9Ez6i0jDJTI1JE8cJkzbin.info/www/bejne/pIKZh5dsha2hr9E

[@Lolwutdesu9000]

Fellow physicist here. Great video, although I need to be a tad pedantic here. The ideal gas assumptions from which the basic gas laws are derived are not "incorrect". Every model in physics, and quite frankly, science as a whole, starts off with some basic assumptions which, if true, lend themselves to helping us build up a picture of reality. Eventually, these models fail under new, yet undiscovered circumstances, and we either adapt or sometimes, if necessary, change these models, although the former is much more likely should the base model work to a good degree. Every, and I mean EVERY model we have today is based on some assumptions, which are all, by the very definition of how we understand nature, our best guesses of reality, hence they are ALL technically incorrect (maybe one day we'll understand the universe and reach some "final" level of understanding, who knows, but I digress). Even the standard model of cosmology is slowly being eroded due to new evidence showing that previous measurements of expansion were just wrong. We must simply understand why models work, and when they fail, why they fail, and how we adapt accordingly.

[@alext5497]

The 'crackpots' have been pointing at the problems in Cosmology for decades.its not the models that are broken, it's the scientific community, the universities, and peer review.

[@ultimatedude5686]

The term "incorrect" was probably just clickbait

[@aniksamiurrahman6365]

Looking forward to an episode on Van Der Waals interactions.

[@Phymacss]

This is simply the best video I’ve seen about this topic. I’ve searched for many videos including drawings or graphics to help visualize the idea and this definitely helped. Many many thanks.

[@tfs711]

Definitely would love to watch van der Waal's equation. And this was so good and still simple 👍👍👍

[@aniksamiurrahman6365]

Johannes Diderik van der Waals is my ideal. Not Maxwell, not Einstein, this Dutch boi - almost a Dutch version of Michael Farady attracts me most.

[@pavlopanasiuk7297]

@@aniksamiurrahman6365 van der Waals'es authority was repelling the community from admitting that wdw gas is not that good as virial expansion. Even when there were enough evidence (significant differences in critical exponents).

[@aniksamiurrahman6365]

@@pavlopanasiuk7297 Well, that was the early day of molecular scince. Such detrimental effect on the early day was common - by Newton on Physics, by Pasteur on Biochemistry and many more. Still Van Der Waals will always be one of the forefather of molecular science.

[@pavlopanasiuk7297]

@@aniksamiurrahman6365 that's true, authority is too much important even nowadays

[@aniksamiurrahman6365]

@@pavlopanasiuk7297 Heh! Authority! Soon after Van Der Waals, molecular science practically came to a halt. Due to Einstein, the entire physics world were busy with Quantum Physics. After Einstein craze settled, WW2 happened and everyone was busy with nuclear physics. Molecular physics only resurrected during the 60s. And as soon as "progress" resumed, people started working out proper theories. But that's not your agenda is it? I doubt that you are an actual Chemist or Physicist or any science grad at all. If you're coming from some shady blog then please stop replying with your nonsense. If you are an American, then that will explain your ailment.

[@pipertripp]

Yep, van der wal vid would be great. Really enjoyed this one. Cheers!

[@garethwilliams2173]

Good video which ended just as it was getting to the really interesting bits.

[@guilhermejung98]

Awesome video! I would love to watch your video on the van der waal's equation.

[@sezkangkhoo44]

Very simplified and precise explanation ! Even better than Atkins textbooks !

[@HerkulesPierewoj]

Great videos! I found your channel while exploring quantum physics as a hobby. Now I'm certain that I will be applying to nuclear physics studies next year! Greetings from 🇵🇱😛

[@DenisIbrahimovic]

Great video, thanks Parth!

[@jennykeeling3716]

This was great 😊 very well explained

[@matthewcarlyon5133]

Would love to see a video about van der Waals gases in the near future!

[@altuber99_athlete]

We also make assumptions in electric circuit theory/analysis (which is what electronics and power engineers use to model circuits), usually known as “the lumped model”. Basically in this way we can use differential equations with scalar functions instead of Maxwell’s equations (differential equations with vector functions, which are harder to solve). Some of these assumptions are that electromagnetic phenomena travel instantly, that magnetic fields don’t leak out of an inductor and electric fields don’t leak out of a capacitor, that the electric circuit is an isolated system from the surroundings, etc.

[@badlydrawnturtle8484]

"Because it doesn't really mean anything for an object that we assume to be infinitely small to rotate" Quantum mechanics is laughing.

[@KaliFissure]

The same way i question the use of a perfect fluid in the application of Friedman equations and suggest that a variable density, pseudoplastic or thixotropic, fluid should be used. The universe appears more viscous at low density and less viscous at high density. Gravity itself could be considered a manifestation of this deeper character. Low viscosity encourages smaller scales of turbulence which would turn large scale rotation like a galaxy edge into curl. Apparently absorbing linear velocity.

[@trueriver1950]

If this approach was found to match observations, then it would raise questions for cosmologists about what is providing the viscosity. Viscosity always implies some kind of "friction" between particles. Thixotropic effects also imply that the same collection of particles in identical positions can have two or more states. That would raise the further question of how that change if state occurred and how the state was "remembered". Given that in cosmology we think in terms of a particle being a galaxtic cluster or something larger still, clearly there is scope to argue that there is some internal state within a particle due to the configuration of its constituent galaxies and/or the internal config of each galaxy. The Friedmann eqns differ from the ideal gas in that they assume that the "particles" do not collide at all ever, and that there are no long range forces between "particles" larger than galaxies (gravity not being counted as a force but as an effect of Riemann curvature). In other words the assumption is that on a scale larger than galaxtic superclusters the Einstein eqns are all we need to consider. This assumption is broadly consistent with observations, though there is a "phase transition" at about 300k years when the universe becomes transparent (ie when the background of photons decouples from the soup of other matetial) I don't immediately see what experimental discrepancy you hope that the introduction of viscocity would address, let alone thixotropy. But if it were found that thixotropic effects made the equations better fit observations it would certainly raise interesting questions for cosmologists... perhaps raising more q's than it solved.

[@BeoFistTie01]

Please Parth bhaiya make a video on vander waal equation soon and also explain PV=nRT and also explain affects of temperature and maxwell distribution of molecular speeds thanks bhaiya you help us all a lot in IIT preparation WITH YOUR AWESOME EXPLANATIONS

[@ronaldshellenberger7118]

It would be awesome if you made a video on a Van der Waals gas!!!

[@topquarkbln]

I like all your videos - please go on! ❤👍

[@miguelcarvalho5941]

I'm starting my thesis and today spent the day working with Kinetic gas theory. KZbin algorithm knows its way around :)

[@deprivedoftrance]

Yes please make the video!

[@girindrasingh1612]

THANKS BROTHER !!

[@sathiroy4506]

Please, Please make a Video on Vander Waals Equation.

[@elaadt]

Thanks for the video. How about statistical mechanics?

[@MK-bs3dq]

Please discuss a sample computation for Ideal gas VS Actual gas. thanks

[@jaganathanjonathon8102]

Yes,, would very much like a video on Van de Waal’s gas, even if I have possibly got the spelling right.

[@sitrakaforler8696]

Haha excellent ! You just summarized HOURS of cours (well not 10 hours but it is still a great overview T^T )

[@abhishekprasad6350]

Just want everyone to know why most of us just learn 2 rotational way of storing energy in di-atomic molecules because of the moment of inertia along the axis which passes through the centre of both atoms is di-atomic molecules are almost negligible because of very small radius along the axis(radius of gyration) Cheers🙃 And, Parth love your videos💖

[@leonardomedel9400]

A really good topic to be explained could be the ensembles, which appear in statistical mechanics; there are important physical ideas around this important concept.

[@BeoFistTie01]

Also bhaiya you can make a video on all the gas laws : Boyle’s law Charles’s law Gay Lussac’s law Avogadro’s law. And explain their graphs for each law. And also Dalton’s & Graham’s law. Thanks 🙏🏻

[@zulqarnainchaughtai]

Wanna see video on Maxwell distribution of velocities!

[@arnesaknussemm2427]

Have you covered entropy?

[@frogandspanner]

It would be useful to explore _why_ the assumptions are made - this is often not treated well at A-level, with students just learning a list of assumptions to regurgitate in the exam.

[@cellotron4758]

As in how exactly the assumptions make the math in Ideal Gases possible?

[@frogandspanner]

@@cellotron4758 Yes. How each assumption helps us simplify the problem.

[@cellotron4758]

@@frogandspanner What exactly are the equations that you guys learn in A-level? Maybe searching up their derivations can help you see how the assumptions are crucial for simplifying the equations.

[@frogandspanner]

@@cellotron4758 I taught the reasons for the assumptions, but many teachers teach to the specification and exam, and exam questions just ask for the assumptions, not the reasons for them. I thought a video could include the reason for the assumptions as it would help A level students who were taught to examination rather than to science.

[@Jehannum2000]

@@frogandspanner Yes, it's a good, valid idea. An explanation of why the assumptions are made would lead naturally to the next level of understanding.

[@boazbarkai8981]

Isn't electro static forces between electrons are actually "collision" between the atoms?

[@sukhmannarula1271]

I wanna see a quantum mechanical ideal has vid

[@deepsahay1080]

I want to see a video on physics behind gyroscope

[@somecreeep]

Could you do a video at some point that gives a good definition of a state of matter? Like what behavior is necessary to conclude that something has changed to a different state of matter? It's always very hand-wavingly described like "well you know when you see it" but there has to be a scientific definition, right?

[@timeussubanath3900]

Hii!! Parth G... Can you answer to this question.. Can we be a Physicist and a Chemist....

[@andrewmorehead3704]

Van der waals equation please!

[@wayneyadams]

Polar molecules cause some of the biggest deviations from the ideal gas law. Water is among the worst gases (actually it is a vapor) when it comes to deviations from the Ideal Gas Law, besides its shape, it is polar, and even worse there is hydrogen bonding. 7:28 Even Van der Waals made some unrealistic assumptions. He assumed that gaseous particles: 1) Are hard spheres. 2) Have definite volume and hence cannot be compressed beyond a limit. 3) Two particles at close range interact and have an exclusive spherical volume around them. The one important fact to remember is that all real gases behave like ideal gases at extremely high temperatures and low pressures.

[@StringerNews1]

"It's not gas pressure, it's atmospheric pressure." --FlerfSpective

[@lexcyrus3017]

How can I ask physics questions

[@SevenNineGuy]

If the ideal gas was a hard sphere it would have a second viral coefficient and therefore not ideal

[@praveenb9048]

Would you care to weigh in on the ongoing chain fountain debate between Steve Mould and Electroboom?

[@trueriver1950]

Relevance here?

[@Ranbir.Bhardwaj]

I came for van der waals equation, How long do I have to wait

[@za1231in]

yo quantum ideal gas sounds wild

[@aki-fi3gk]

First Good job parth

[@geeache1891]

Inelastic collisions, at a quantum level?

[@tdoc9051]

B4 watching im just gna say 'perfectly elastic particle collisions'

[@gustavobier827]

Recommend this video about how to simulate an ideal gas: kzbin.info/www/bejne/anzXgmqDgtmgaJo

[@macleadg]

I assumed an ideal gas was a fart that smelled like perfume. Apparently that’s wrong. (Ok, I’ll leave before the bouncer tosses me).

[@aMartianSpy]

I was looking for this sort of comment... 😁

[@macleadg]

@@aMartianSpy I’m in close touch with my inner middle-schooler.

[@ParthGChannel]

Hahaha

[@jeffgorman9353]

Maybe a fart that contains a tiny bit of skatole? Careful, though, too much and you tip the balance from perfume to shart.

[@nehaseth2793]

Great

[@nirmankhan2134]

⚡⚡

[@nehaseth2793]

@@nirmankhan2134 😎

[@soumyaranjanmohapatra3742]

👌👌👌

[@rupeshchoudhari96]

Wow

[@mr.winter538]

I know this is a stupid idea, but could we make a macroscopic ideal gas? That is, could we make a huge container in space with loads of spheres, consisting of a hypothetical material that is both incredibly hard and exceedingly good at exchanging kinetic energy with an extremely high melting point, in it and expect it to act even remotely similar to how a ideal gas would work?

[@PMA65537]

You need high numbers of particles for the statistics to work.

[@pappa6085]

neutral atoms don't repel,,, they actually may snap,, because wen, for instance, a hydrogen atom touches another hydrogen atom, the electron of atom a will be attracted by the nucleus of atom b and vise versa,, and thus H2 is formed

[@Jehannum2000]

How about helium?

[@carultch]

They do repel very locally. The force adds up to zero when they are significantly far apart. But the parts of the electron shells that are closer to each other than they are to the nucleus of the other atom, are what does the repelling.

[@omeritachiquita]

😙👌

[@curtdeno1146]

I would like you to at least motivate the ideal gas law, not stop with the key assumptions. Your clarity of presentation would benefit this. Thanks.

[@mansi1083]

Please do not beg for subscribers ...again nd again😐otherwise every video is awesome

[@djamshid9172]

"... a gas is made up of a lot of little PARTH-G-icles..." :p

[@jaganathanjonathon8102]

Haven’t got the spelling right, Sorry!

[@emamulhasan]

proparties,

[@lamarozzo]

That's not 100% correct. What you are describing is the dilute limite of the hard sphere model, where particles bounce off elastically. In the ideal gas model there are no interactions between the particles, so they can't be hard spheres (no matter how small). You did mentioned that there should be no interactions, which contradicts your earlier statement that particles should be small spheres. Also, the ideal gas model doesn't assume that the particle is a single atom. Bi-atomic or Poly-atomic gases can be ideal gases as long as they don't interact with each other. Technically this is because the internal partition function of a molecule does not depend on the system volume, so it doesn't contribute to the pressure. To sum it up: the ideal gas assumption is that there are no interaction between the constituents of the gas. As long as temperatures are high enough to avoid quantum statistics that's all you really need to define a classical ideal gas.

[@nissemus]

This video is a real gas.

[@polyrhythmia]

And then there's steam or water vapor.

[@hrimonrakshit6840]

Tell me the kinetic theory without telling me the kinetic theory 😁

[@cogwheel42]

I think you have elastic and inelastic backwards. Elastic collision is like a rubber ball which *does* compress. Inelastic is like a billiard ball or ideal gas atom.

[@hipphipphurra77]

Elastic (collision) does not mean that there is no deformation. This statement is wrong.

[@mnada72]

I am 222 👍

[@Jehannum2000]

Happy birthday, old boy.

[@Metaldetectiontubeworldwide]

if find all gases ... far from ideal ...lol

[@theimmux3034]

engineer

[@timeussubanath3900]

Hii!! Parth G... Can you answer to this question.. Can we be a Physicist and a Chemist....

[@timeussubanath3900]

Hii!! Parth G... Can you answer to this question.. Can we be a Physicist and a Chemist....

[@timeussubanath3900]

Hii!! Parth G... Can you answer to this question.. Can we be a Physicist and a Chemist....

[@timeussubanath3900]

Hii!! Parth G... Can you answer to this question.. Can we be a Physicist and a Chemist....