State the assumption about ideal gas molecules in terms of how they move.
State the assumption about ideal gas molecules in terms of their volume.
A cube with volume $V$ contains $N$ molecules of an ideal gas. Each molecule has a velocity component $c_x$ perpendicular to one face $S$ of the cube, as shown in Fig. 2.1. The pressure $p$ of the gas due to the component $c_x$ of velocity is given by the expression $pV = Nmc_x^2$, where $m$ is the mass of a molecule. Explain how this expression leads to $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $\langle c^2 \rangle$ is the mean square speed of the molecules.
An ideal gas has a root-mean-square (r.m.s.) speed of $520\,\text{m s}^{-1}$ when its temperature is $27^\circ\text{C}$. Calculate the r.m.s. speed of the molecules when the temperature is raised to $100^\circ\text{C}$.