[Physics] How do gas molecules break newton’s laws of motion

kinetic-theorynewtonian-mechanics

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.

Best Answer

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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