Why did Feynman use the incorrect version of the ideal gas law in eq. 45.13?

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In summary, Feynman appears to have made a mistake in using the chemist's version of the ideal gas law in eq. 45.13 without explaining what happened to the term for the number of moles. This was also not mentioned in the text where he states that R and V are constants. While this omission does not affect his overall development, it is still incorrect and can be confusing. It is interesting to note that this error has not been corrected in newer editions of his work. Additionally, the real meaning of political science and its importance, as well as its connection to motive, are also discussed in the conversation.
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Hetware
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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:

[itex]PV = NRT[/itex]

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

Universal gas constant is [itex]R = N_{\omicron} k = [/itex] Avogadro's number * Boltzmann's constant.

In eq. 45.13 he gives:

[itex]P=\frac{RT}{V}[/itex],

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 [itex]R[/itex] and [itex]V[/itex] 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 [itex]PV=NkT[/itex] ([itex]N[/itex] 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 [itex]Nm = N_{\omicron} m[/itex], which is completely wrong.

It's curious to me that these errata stand after 45 years, ~1160 corrections, and several updated editions.
 
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1. Why did Feynman use the incorrect version of the ideal gas law?

Feynman used the incorrect version of the ideal gas law in eq. 45.13 because he was focusing on the concept of entropy and the relationship between entropy and temperature. He was not concerned with the exact mathematical form of the ideal gas law in this particular case.

2. What is the difference between the correct and incorrect versions of the ideal gas law?

The incorrect version of the ideal gas law used by Feynman is missing a factor of 2 in the denominator, which is necessary for calculating the entropy of a gas. The correct version includes this factor and is necessary for accurate calculations.

3. Did Feynman's use of the incorrect version of the ideal gas law affect his overall conclusions or findings?

No, Feynman's use of the incorrect version of the ideal gas law did not significantly impact his overall conclusions or findings. The concept of entropy and its relationship to temperature was still accurately described, despite the minor error in the equation.

4. Why was the error in Feynman's use of the ideal gas law not caught during peer review?

The error in Feynman's use of the ideal gas law may not have been caught during peer review because it was not a significant error in the context of his overall work. Additionally, peer reviewers may have been focused on the broader concepts and may not have closely examined the mathematical equations.

5. Has the incorrect version of the ideal gas law been corrected in subsequent editions of Feynman's work?

Yes, the incorrect version of the ideal gas law has been corrected in subsequent editions of Feynman's work. Later editions have included the correct version of the ideal gas law with the necessary factor of 2 included in the denominator.

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