Chapter 22: Problem 14
The speeds of a group of ten molecules are \(2.0,3.0,4.0, \ldots\), \(11 \mathrm{~km} / \mathrm{s}\). ( \(a\) ) Find the average speed of the group. (b) Calculate the root-mean-square speed of the group.
Chapter 22: Problem 14
The speeds of a group of ten molecules are \(2.0,3.0,4.0, \ldots\), \(11 \mathrm{~km} / \mathrm{s}\). ( \(a\) ) Find the average speed of the group. (b) Calculate the root-mean-square speed of the group.
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Get started for freeShow that the constant \(a\) in the van der Waals equation can be written in units of \(\frac{\text { energy per particle }}{\text { particle density }}\)
Calculate the root-mean-square speed of smoke particles of mass \(5.2 \times 10^{-14} \mathrm{~g}\) in air at \(14^{\circ} \mathrm{C}\) and \(1.07\) atm pressure.
At what frequency would the wavelength of sound be on the order of the mean free path in nitrogen at \(1.02\) atm pressure and \(18.0^{\circ} \mathrm{C} ?\) Take the diameter of the nitrogen molecule to be \(315 \mathrm{pm}\)
You are given the following group of particles \(\left(N_{n}\right.\) represents the number of particles that have a speed \(v_{n}\) ): $$\begin{array}{lc}N_{n} & v_{n}(\mathrm{~km} / \mathrm{s}) \\\\\hline 2 & 1.0 \\\4 & 2.0 \\\6 & 3.0 \\\8 & 4.0 \\\2 & 5.0\end{array}$$ (a) Compute the average speed \(v_{\mathrm{av}} .(b)\) Compute the rootmean- square speed \(v_{\text {rms. }}\) (c) Among the five speeds shown, which is the most probable speed \(v_{\mathrm{p}}\) for the entire group?
Show that, for atoms of mass \(m\) emerging as a beam from a small opening in an oven of temperature \(T\), the most probable speed is \(v_{\mathrm{p}}=\sqrt{3 \mathrm{kT} / \mathrm{m}}\).
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