I was reading about the Kinetic Theory of Gases and I came to know about This Particular equation which piqued my interest.

I know about the Ideal Gas Law which gives us $PV=nRT$.
But this one contained Boltzmann's Constant and it goes like this $PV=Nk_BT$ where $k_B$ is the Boltzmann constant and T the absolute temperature.
Could I get some insights to how was this form of Ideal Gas Law Derived? And how was the value of $k_B$ and $R$ determined ? Any help would be appreciated.


1 Answer 1


$R$ is defined as $k_{B}N_{A}$ where $N_{A}$ is Avogradro's number. Notice that these forms are equivalent once you realize that $N = N_{A}n$.

I think $k_{B}$ is measured experimentally. I learned the derivation via statistical mechanics.

  • $\begingroup$ Thanks for your help.......I never noticed this while I was searching on Wikipedia $\endgroup$
    – user35508
    Nov 2, 2016 at 15:40

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