# 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. Feb 6, 2017 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 Feb 6, 2017 at 14:34
• The argument about whether "Newton's second law is definition" has not been settled yet. See this journal Feb 6, 2017 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. Feb 6, 2017 at 15:23
• 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.
– Arc
Jan 16, 2022 at 1:40