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I was reading up on the Ideal Gas Equation in University Physics with Modern Physics by Young and Freeman when I chanced upon a seemingly illogical mathematical equation.

Can anyone rectify this error? Or is it misunderstanding on my part?

Here is the portion (Page 600, Chapter 18, Equation 18.12):

$$pV = \frac{1}{2}Nm(v^2)_{av} = \frac{1}{3}N\biggl[\frac{1}{2}m(v^2)_{av}\biggr]$$

It should be clear that $\frac{1}{3} \neq (\frac{1}{3} \times \frac{1}{2})$.

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Oh, and is it possible for someone to provide the correct equation? Thanks! –  Yuruk May 10 '13 at 7:24
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up vote 5 down vote accepted

Nice catch!

For reference here is the book page.

:enter image description here

See , though it may error in printing or anything else.The final equation they get $$pV=\dfrac23K_{tr}$$ is very correct.

The correct form of $eq.(18.12)$ must be $$pV=\dfrac13Nm(v^2)_{av}=\dfrac {\color{red}{\huge{2}}}3N\bigg[\dfrac12 m (v^2)_{av}\bigg]$$

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Thanks! For a moment I thought my mathematics education had failed me. –  Yuruk May 11 '13 at 2:37
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