In $PV=nRT$, $n$ is degrees of freedom. While in $PV=Nk_BT$, N is number of moles in a molecule. So value of $n$ is $3$, $5$ and $6$ for monatomic, diatomic and polyatomic respectively. But in the video, he wrote that $n=1$ for monatomic. Isn't that a wrong assumption?
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1$\begingroup$ You have several errors in your post. N is the number of molecules, n is the number of moles. "The number of moles in a molecule" is nonsense. $\endgroup$– nasuCommented Feb 11, 2022 at 12:31
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$\begingroup$ You've completely misunderstood the terms "n" and "N". $\endgroup$– CrossCommented Feb 11, 2022 at 12:35
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In the ideal gas law $$PV=nRT$$ $n$ is not the degrees of freedom. Instead $n$ is the number of molecules (measured in mol). You can see this also from the unit of the gas constant $$R=8.314 \text{ m}^3\text{ Pa}\text{ K}^{-1}\text{ mol}^{-1}$$
answered Feb 11, 2022 at 12:34