You, sir, deserve a medal. Man, you're way better not only than my lecturer, but also than the textbook, as well :p btw, I only signed in to like your video and write this comment :)
Nobel prize should NOT be given to him because he doesn't clarify his explanations for people in the comments. E.g. he didn't bother to consider my long comment in which I showed some contradictions of his explanation.
Thank you for your reply but I don't get it. Higher than what? And how high is higher? As it is said, each degree of freedom should have an average energy of kT/2. So I don't understand why we don't take into account the vibrational degree of freedom. It should have the same average energy. And since an oscillations have two degrees of freedom, energy associated with them should be equal to 2*(kT/2)=kT.
IMdigitalworks--The temperature depends on the composition of the gas. If you're in a typical physics course, you most likely won't encounter a problem where you have to account for the vibrational degrees of freedom. If there is a case where you do have to account for it, then it should be made evident in the wording of the problem you're working on. Just know that to get molecules to vibrate, you need a significant amount of heat energy to do so.
I'm not working on any particular problem, I just want to understand this "principle of equipartition of energy". Ok, I know, this should be true: "to get molecules to vibrate, you need a significant amount of heat energy to do so". But then I do not understand the concept of "equipartition of energy". If energy is partitioned equally among those degrees of freedom, then why vibrations get their part only when temperatures are high? Let's say, I have only one diatomic molecule in a container. If I put an energy equal to 70 (in some units) to my "single molecule gas container", I wonder how this amount of energy would be distributed among the degrees of freedom of the molecule. 1) If we do not account for vibrations, then we have 5 degrees of freedom (3 translations, 2 rotations) and each degree of freedom gets an energy equal to 70/5=14. Since 14=kT/2, we can define the temperature of the system which is T=28/k. 2) If we account for vibrations, then we have 7 degrees of freedom, each of them getting the energy equal to 70/7=10 and the temperature for the system is 20/k. So the temperature depends on whether we take vibrations into account or not. That's weird. And how to know if the molecule would vibrate or just move around?
Keep in mind, I am just a student learning this for the first time as well but as far as your statement, "If energy is partitioned equally among those degrees of freedom, then why vibrations get their part only when temperatures are high?". -You have to account for the kinetic energy of vibrations when vibrations are occurring in a gas. Because, it is only at higher temperatures (whatever that temperature may be) that molecules begin vibrating. You can have a diatomic molecule at some medium temperature and you will find that both experimentally and theoretically, they will have 5 degrees of freedom--they will not vibrate because they are not energized enough to vibrate. But if you put more energy in the system, such as more heat, then it will increase their temperature and, since temperature is a measure of kinetic energy, it is another way of saying that you increased their kinetic energy and some of that energy goes into speeding up their translational kinetic energy and some goes into vibrational kinetic energy. Why this happens at higher temperatures, depends on their bond/properties. And for your two other points. It makes sense that each degree of freedom has less temperature because think about it, if you put in say 70 Joules of energy in the system, then those 70 joules are equally partitioned into the 5 and 7 degrees of freedom, but the energy change till adds up to 70 J. Think of it this way: Say a truck that is moving, has 70 J of kinetic energy, and is driving on a frictionless road and any collision is totally elastic. Now let's say that it hits a row of 5 (synonymous with the 5 degrees of freedom) cars, and the collision made the truck stop, transferring its 70 Joules of KE into the 5 cars. If you look at each cars kinetic energy, it will have 70/5= 14 J of kinetic energy, so you can say that the temperature of each degree of freedom contributes 28/k, so 5*(28/k)=140/k for the particle. Say there are 7 cars now (synonymous with 7 degrees of freedom) then each car now only has 70/7 = 10 J of kinetic energy. So degree of freedom contributes to 20/k of temperature to the particle, so that particle has a temperature of 7*(20/k)=140/k, the same NET temperature of the particle. To know if there are 5 or 7 cars that the energy is partitioned into, then you have to analyze the diatomic molecule by some means to know when and at what temperature the vibrations are activated. Hope you found this helpful and that I didn't confuse you. This is the best I can do to explain.
The Equipartition theory is flawed especially at the low end as it implies a molecule can move in three different directions at the same time which is impossible. They get around the problem by claiming the 3 dimensional energy. the Kinetic Energy, applies to a system of molecules but it is just a ends justifying the means explanation. There is a newer and more reasonable explanation for the storage of energy in gas molecules.
+JediSawyer The equipartition theorem fails because the internal energy of molecules is quantized and so when the spacings of the energy levels are larger than KT, it breaks down because the energy can't be transferred by collisions. For small energy level spacings, it is a close enough approximation to model nature.
You, sir, deserve a medal. Man, you're way better not only than my lecturer, but also than the textbook, as well :p
btw, I only signed in to like your video and write this comment :)
Nobel price should be given to you in the field of the fastest and easiest explanations of Modern Physics topics :D
Farid Mammadov 😂😂 i totally support this
Nobel prize should NOT be given to him because he doesn't clarify his explanations for people in the comments. E.g. he didn't bother to consider my long comment in which I showed some contradictions of his explanation.
You rock!!! That's by far the best explanation one can find on earth... Hat taken off for you
Why can every professor explain like you do!? There would be no need to study so hard for tests, we would just recall everything... Thank you!!!!
Gabriela Rodriguez
You literally save my life on the daily
Well explained in a simple language and easily to understand...Excellent work Sir!!!
Thank you so much sir👏👏👏
GOT IT!!!! THANK YOU!
awesome!! Thank you so much :)
You saved me yet again
Thank you sir!
Never gets old....
Thank you very much.
Very well done
bravo!
Amazing, than you!
You are awesome
Thanks so much. My book confuses me so much on this topic.
ty men
Doesn't monoatomic moleciule have vibrational motion sir( like simple harmonic motion in physics)
No
Sir why didn't you consider rotational motion in yz plane
Cause the momento of inertia is small(I suppose)
We can only define internal energy as the difference between final and initial internal energies of a particular system.
🤦♀........... I m unable to understand anything.... ☹️
You still didn't tell where the kT/2 comes from.
Why we do not take into account the vibrational degree of freedom?
I depends on the temperature. You account for vibrations at higher temperatures.
Thank you for your reply but I don't get it. Higher than what? And how high is higher? As it is said, each degree of freedom should have an average energy of kT/2. So I don't understand why we don't take into account the vibrational degree of freedom. It should have the same average energy. And since an oscillations have two degrees of freedom, energy associated with them should be equal to 2*(kT/2)=kT.
IMdigitalworks--The temperature depends on the composition of the gas. If you're in a typical physics course, you most likely won't encounter a problem where you have to account for the vibrational degrees of freedom. If there is a case where you do have to account for it, then it should be made evident in the wording of the problem you're working on. Just know that to get molecules to vibrate, you need a significant amount of heat energy to do so.
I'm not working on any particular problem, I just want to understand this "principle of equipartition of energy". Ok, I know, this should be true: "to get molecules to vibrate, you need a significant amount of heat energy to do so". But then I do not understand the concept of "equipartition of energy". If energy is partitioned equally among those degrees of freedom, then why vibrations get their part only when temperatures are high?
Let's say, I have only one diatomic molecule in a container. If I put an energy equal to 70 (in some units) to my "single molecule gas container", I wonder how this amount of energy would be distributed among the degrees of freedom of the molecule.
1) If we do not account for vibrations, then we have 5 degrees of freedom (3 translations, 2 rotations) and each degree of freedom gets an energy equal to 70/5=14. Since 14=kT/2, we can define the temperature of the system which is T=28/k.
2) If we account for vibrations, then we have 7 degrees of freedom, each of them getting the energy equal to 70/7=10 and the temperature for the system is 20/k.
So the temperature depends on whether we take vibrations into account or not. That's weird. And how to know if the molecule would vibrate or just move around?
Keep in mind, I am just a student learning this for the first time as well but as far as your statement, "If energy is partitioned equally among those degrees of freedom, then why vibrations get their part only when temperatures are high?".
-You have to account for the kinetic energy of vibrations when vibrations are occurring in a gas. Because, it is only at higher temperatures (whatever that temperature may be) that molecules begin vibrating. You can have a diatomic molecule at some medium temperature and you will find that both experimentally and theoretically, they will have 5 degrees of freedom--they will not vibrate because they are not energized enough to vibrate. But if you put more energy in the system, such as more heat, then it will increase their temperature and, since temperature is a measure of kinetic energy, it is another way of saying that you increased their kinetic energy and some of that energy goes into speeding up their translational kinetic energy and some goes into vibrational kinetic energy. Why this happens at higher temperatures, depends on their bond/properties.
And for your two other points. It makes sense that each degree of freedom has less temperature because think about it, if you put in say 70 Joules of energy in the system, then those 70 joules are equally partitioned into the 5 and 7 degrees of freedom, but the energy change till adds up to 70 J. Think of it this way:
Say a truck that is moving, has 70 J of kinetic energy, and is driving on a frictionless road and any collision is totally elastic. Now let's say that it hits a row of 5 (synonymous with the 5 degrees of freedom) cars, and the collision made the truck stop, transferring its 70 Joules of KE into the 5 cars. If you look at each cars kinetic energy, it will have 70/5= 14 J of kinetic energy, so you can say that the temperature of each degree of freedom contributes 28/k, so 5*(28/k)=140/k for the particle.
Say there are 7 cars now (synonymous with 7 degrees of freedom) then each car now only has 70/7 = 10 J of kinetic energy. So degree of freedom contributes to 20/k of temperature to the particle, so that particle has a temperature of 7*(20/k)=140/k, the same NET temperature of the particle.
To know if there are 5 or 7 cars that the energy is partitioned into, then you have to analyze the diatomic molecule by some means to know when and at what temperature the vibrations are activated.
Hope you found this helpful and that I didn't confuse you. This is the best I can do to explain.
Meh you're not that good....YOU'RE AWESOME
Frosty Snow Thanks Frosty! :-)
The Equipartition theory is flawed especially at the low end as it implies a molecule can move in three different directions at the same time which is impossible. They get around the problem by claiming the 3 dimensional energy. the Kinetic Energy, applies to a system of molecules but it is just a ends justifying the means explanation. There is a newer and more reasonable explanation for the storage of energy in gas molecules.
+JediSawyer
The equipartition theorem fails because the internal energy of molecules is quantized and so when the spacings of the energy levels are larger than KT, it breaks down because the energy can't be transferred by collisions. For small energy level spacings, it is a close enough approximation to model nature.