Veracity of Simple Molecular Model

[Bashyboy]

Hello Everyone,

I understand that sometimes in physics we make a model of some physical system purely for theoretical convenience, as it allows us to calculate certain properties of the system very easily; although, sometimes these models aren't actually what is going on, but it doesn't matter, so long as the model accurately predicts the effects.

In the given link http://www.phy.duke.edu/~lee/P53/therm2.pdf , they suppose such a model. Here is what they say:

"To be able to count the degrees of freedom we must make a model of the molecule. We
will treat the atoms as point masses, and imagine that the bonds between atoms are like
stiff springs connecting these masses."

How accurate is this model, and when does it begin to break down?

 

[DrClaude]

In the given link http://www.phy.duke.edu/~lee/P53/therm2.pdf , they suppose such a model. Here is what they say:

"To be able to count the degrees of freedom we must make a model of the molecule. We
will treat the atoms as point masses, and imagine that the bonds between atoms are like
stiff springs connecting these masses."

How accurate is this model, and when does it begin to break down?

It works pretty well so long as quantum effects are not important. This most often means big systems ($\sim N_\mathrm{A}$) and high temperatures. Basically, you want the difference between consecutive energy levels to be small compared to $k_\mathrm{B} T$, and that the probability of a single quantum state to be populated to be $\ll 1$.

If you want to know more, you should look into statistical physics. An introductory course will cover quantum statistics and the classical limit.

 

[Bashyboy]

So, would it be safe to say, that this model will probably work in almost all cases in which someone uses thermal physics?

I actually just began such a course. But I believe we won't be covering those topics for some time.

 

[DrClaude]

So, would it be safe to say, that this model will probably work in almost all cases in which someone uses thermal physics?

Yes. For a gas, so long as you don't start doing things like laser cooling, that model is a pretty good description. Deviations from the ideal gas law due to interactions between molecules will kick in much before that model of point masses and springs is no longer valid.