# How do gas molecules break newton's laws of motion

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.

• Unless you need to take quantum mechanics and relativity into accounts, I can't see the reason of violation of Newton's law behind. – Ng Chung Tak Feb 6 '17 at 14:20
• @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 – Suhrid Mulay Feb 6 '17 at 14:34
• The argument about whether "Newton's second law is definition" has not been settled yet. See this journal – Ng Chung Tak Feb 6 '17 at 14:53
• 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. – Jon Custer Feb 6 '17 at 15:23

## 1 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.