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In my book on the chapter about KTG (Kinetic Theeory of Gases) and thermodynamics It is mentioned that KTG assumes an assumption:

  • All gas molecules follow newton's laws of motion.(This however is not valid for all cases)

When I ask my mentor about this he says that the line refers to Newton's Second law of motion. (However he abstained from further answering my doubts citing time constraints.).

However as far I understand newtons second law is:

Impressed force is directly proportional to rate of change of momentum. Mathematically:

$$ \vec{F} = \frac{d\vec{p}}{dt}$$

Which to me appears a mathematical definition of force And I don't see how a definition can be violated. Which is confusing. Any help would be nice.

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    $\begingroup$ Unless you need to take quantum mechanics and relativity into accounts, I can't see the reason of violation of Newton's law behind. $\endgroup$ Commented Feb 6, 2017 at 14:20
  • $\begingroup$ @NgChungTak. but newtons laws (Specifically the second one) is a (Mathematical) definition of force. Regardless of whatever science or physics you use it should stay the same because its a definition $\endgroup$ Commented Feb 6, 2017 at 14:34
  • $\begingroup$ The argument about whether "Newton's second law is definition" has not been settled yet. See this journal $\endgroup$ Commented Feb 6, 2017 at 14:53
  • $\begingroup$ In complete kinetic theory, the center of mass of the molecules (possibly polyatomic) follows classical mechanics, but the internal energy states (rotation, vibration, excitation) would have to be treated quantum mechanically. For dilute gases at room temperature the internal energy states are not a huge contribution to the overall energy. $\endgroup$
    – Jon Custer
    Commented Feb 6, 2017 at 15:23
  • $\begingroup$ Newton's second law is not simply a definition, it stablishes that accelaration is what drives movement, and its not violated in theoretical KTG, unless you derive KTG in the wrong way. I assume the book you mention is this? I found no mention to violations to Newton's laws there. $\endgroup$
    – Arc
    Commented Jan 16, 2022 at 1:40

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Kinetic theory of gases is basically a pure classical theory of a system of non-interacting particles. In such a case, the collision of the particles with each other (which can be assumed to be elastic for very good approximation), and that will the container walls (giving rise to pressure) can be explained well using Newton's laws of motion. I will tell you about why this is not the case always.

When it comes to interacting particles like the electron gas, the kinetic theory fails. This you can find anywhere in books on solid state physics or condensed matter physics (about the failure of Drude model which used kinetic theory to the electron gas to explain electrical conduction). In such a case, one needs sophisticated tools like quantum mechanics to deal with interaction between the electrons. Also, as indicated in one of the comments, when the particles are in relativistic motion, simple mechanics cannot get into the details.

If you can negotiate with the above details, then kinetic theory is affordable to a very good extend.

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  • $\begingroup$ You can use the kinetic theory of gases to treat a gas with collisions, see here. Also, the kinetic theory of gases at first was never meant to be applied to electrons, since they behave quantum mechanically. The Drude model is useful in reaching some very basic results for metals as Ohm's and Wiedemann–Franz law. As a teaching assistant in a course on semiconductors, the Drude model was the first topic we engaged. As with any model, we must learn to recognize its limitations. $\endgroup$
    – Arc
    Commented Jan 16, 2022 at 1:53

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