I know that measurements have established the following(adsbygoogle = window.adsbygoogle || []).push({});

empirical laws for the ideal gas, contained in some closed volume:

-Keeping pressure and temperature constant, the volume is proportional to the number of moles.

-The volume varies inversely with pressure.

-The pressure is proportional to the absolute temperature.

These three relations can be put in an equation, called the ideal-gas equation:

[tex]pV=nRT[/tex]

where the constant of proportionality is the gas constant.

As far as I have understood, R is an experimentally measured quantity:

[tex]R=8.314510(70) J/mol\cdot K[/tex]

when we want to work with the number of particles instead of moles (which we often do) wedefine:

[tex]k=\frac{R}{N_A}[/tex]

where [itex]N_A[/itex] is Avogadro's number and k is called the Boltzmann constant.

The gas equation then becomes:

[tex]pV=NkT[/tex]

with N the number of particles.

These laws can be 'derived' or 'proven' from statistical mechanics.

When applying statistical considerations to the ideal gas and derive the Maxwell-Boltzmann distribution we end up with two constants.

One has to be found by normalization to give the right number of particles and the other one is found by comparing with the above gas equation and they find the Boltzmann constant (times temperature).

So am I correct that the Boltmann constant is (essentially) an experimental value? It occurs to me this constant should be derivable by statistical methods as well.

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# What is the origin of Boltzmann's constant?

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