David Sang and Graham Jones Solutions for Chapter: Ideal Gases, Exercise 6: Questions

Check that the SI base units on the left-hand side of the equation $p=\frac{1}{3}\left(\frac{Nm}{V}\right)<c^2>$ are the same as those on the right-hand side.

The quantity $\mathrm{Nm}$ is the total mass of the molecules of the gas, i.e. the mass of the gas. At room temperature, the density of air is about $1.29 \mathrm{kg}{ \mathrm{m}}^{-3}$ at a pressure of ${10}^5 \mathrm{Pa}$. Use these figures to deduce the value of $<{\mathrm{c}}^2>$ for air molecules at room temperature.

The quantity $\mathrm{Nm}$ is the total mass of the molecules of the gas, i.e. the mass of the gas. At room temperature, the density of air is about $1.29 \mathrm{kg}{ \mathrm{m}}^{-3}$ at a pressure of ${10}^5 \mathrm{Pa}$. Find a typical value for the speed of a molecule in the air by calculating $\sqrt{<c^2>}$. How does this compare with the speed of sound in air, approximately $330 \mathrm{m}{ \mathrm{s}}^{-1}$ ?-