Solution to 2001 Problem 48

In Giancoli section 18-1, it is derived that if the average kinetic energy of a gas molecule is denote by \bar{K},
\begin{align}\bar{K} = \frac{1}{2} m v_{rms}^2 = \frac{3}{2}k T\end{align}
This implies that

\setcounter{equation}{1}\begin{align}v_{rms} = \sqrt{\frac{3 k T}{m}}\end{align}
\setcounter{equation}{2}\begin{align}\frac{v_{rms}\left(N_2 \right)}{v_{rms}\left(O_2 \right)} = \frac{\displaystyle\sqrt{\fr...
The temperatures for the two gases are assumed to be the same, because they are both in the same mixture. Therefore,
\setcounter{equation}{3}\begin{align}\frac{v_{rms}\left(N_2 \right)}{v_{rms}\left(O_2 \right)} = \sqrt{\frac{m\left(O_2 \righ...

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