An ideal gas is taken to contain molecules that are hard elastic identical spheres. State two more assumptions of the kinetic theory of gases.
The number of molecules per unit volume in an ideal gas is $n$. If every molecule is assumed to move at speed $v$, the pressure $p$ exerted by the gas on the vessel walls is given by $p = \frac{1}{3}nmv^2$, where $m$ is the mass of one molecule. Explain how this result is changed to obtain the formula $p = \frac{1}{3}nm\langle c^2 \rangle$.
An ideal gas has density $1.2\,\text{kg m}^{-3}$ when the pressure is $1.0 \times 10^5\,\text{Pa}$ and the temperature is $27^{\circ}\text{C}$. Calculate the root-mean-square (r.m.s.) speed of the molecules of the gas at $27^{\circ}\text{C}$.
Calculate the mean-square speed of the molecules at $207^{\circ}\text{C}$.
Calculate the mean-square speed of the molecules when the temperature is $207^{\circ}\text{C}$.