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ideal gas law due to interactions between molecules will kick in much before that model of point masses and springs is no longer valid.

 

[PJC01]

I can say that the simple molecular model described in the given link is a commonly used and accepted model in physics. It is a simplified representation of a complex system, and as mentioned, it is used for theoretical convenience. However, like any model, it has its limitations and may not accurately represent the actual system in all cases.

The accuracy of this model depends on the specific system being studied and the level of detail required for the calculations. In some cases, this model may accurately predict the behavior of the system, while in others, it may fail to capture all the complexities and nuances of the actual system.

One of the major limitations of this model is that it assumes that atoms are point masses and the bonds between them are rigid springs. In reality, atoms have a finite size and bonds can exhibit flexibility and deformability. This model may also not take into account the effects of other forces such as Van der Waals interactions or hydrogen bonding, which can significantly affect the behavior of a molecule.

In conclusion, while the simple molecular model described in the given link may be a useful tool for calculations, it is important to understand its limitations and when it may break down. As scientists, we must constantly evaluate and improve our models to better understand the complexities of the physical world.