# Feynman eq. 45.13 PV=RT

1. Nov 8, 2012

### Hetware

I've noticed that Feynman appears to have incorrectly used the chemist's version of the ideal gas law. In eq. 39.23 he states it correctly:

$PV = NRT$

Pressure * Volume = Number of moles * Universal gas constant * Temperature

Universal gas constant is $R = N_{\omicron} k =$ Avogadro's number * Boltzmann's constant.

In eq. 45.13 he gives:

$P=\frac{RT}{V}$,

without any explanation as to what happened to the term for the number of moles. He also fails to mention it in the text where he states that $R$ and $V$ are constants. That omission is of little consequence to his development because he is trying to show that pressure is proportional to temperature when volume is held fixed.

But it is still wrong, and was very confusing to me when I read it years ago.

He obviously prefers $PV=NkT$ ($N$ being number of molecules in this case). Apparently he had the incorrect form stuck in his head, because he uses it again when going from eq. 47.23 to 47.24. Again, he ended up with the correct answer, but his reasoning is invalid. What he presents amounts to saying $Nm = N_{\omicron} m$, which is completely wrong.

It's curious to me that these errata stand after 45 years, ~1160 corrections, and several updated editions.

2. Nov 8, 2012