# Is Boltzman's Constant related to the Fine Structure Constant?

what_are_electrons
Is Boltzmann's Constant related to the Fine Structure Constant?

Is Boltzmann's constant related to the Fine Structure Constant and if so how?

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kichigai
That's an interesting question, but what made you think they are related? I'd like to know if the Boltzman constant applies to particles and quantum stuff cause from my reading it applies to gas molecules in a state of equilibrium and involves entropy. Can anyone help a bit? I'm way outa my depth here.

For an ideal gas in which there are no electric forces between gas molecules I would say the answer is no.For real gases the answer is no because by the relation E =k x T if the fine structure constant changed
(and there is no evidence that it does!) then the electric forces between molecules would change, and the kinetic energy of molecules would change and therefore the temperature of molecules would change, but the energy would change in step and so k =E/T would give the same value of the boltzmann constant (about 10^-23 JK^-1).

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There is of course Einstein relation : $$\frac{D}{\mu}=\frac{kT}{e}$$ relating the diffusion coefficient $$D$$ and the mobility $$\mu$$ to the temperature $$T$$ involving Boltzmann's $$k$$ and the electric charge $$e$$.

Although it is a beautiful realtion, this does not involve the fine strucure constant :tongue2:

Also relevant is the fact that the fine-structure constant is dimensionless, while the Boltzmann constant is merely a conversion factor, depending on your choice of units.

So of hand, no, I don't think there is a relationship.

Is it true that Fine structure constant changes at higher energies, if so does anyone know why

what_are_electrons
humanino said:
There is of course Einstein relation : $$\frac{D}{\mu}=\frac{kT}{e}$$ relating the diffusion coefficient $$D$$ and the mobility $$\mu$$ to the temperature $$T$$ involving Boltzmann's $$k$$ and the electric charge $$e$$.

Although it is a beautiful realtion, this does not involve the fine strucure constant :tongue2:
The FSC = e*e / 4pi*epsilon(zero)*hbar*c

epsilon(zero) can be written in terms of mu(zero), so there is that avenue for interaction.

But, to tell the truth, the book I was reading and learning from had a typo in it and they used the term "k" for both the constant of Coulomb's law and the Boltzmann constant. For the Coulomb law equation they showed that k=1/4pi*alpha*epsilon(zero). The presence of the "alpha" caused me to ask this question.

Bottomline: Please take a look at the new thread I started in the General Physics section titled "Coulomb Force Law and the Fine Structure Constant - Variance? " which asks several questions about the Coulomb Law, the Fine Structure Constant and QED.

My apologies for the not realizing their error sooner.