State what the term internal energy means.
State the basic assumption in the kinetic theory of gases that allows you to conclude that there is zero potential energy between the molecules of an ideal gas.
The pressure $p$ and volume $V$ of an ideal gas satisfy $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $N$ is the number of molecules, $m$ is the mass of a molecule and $\langle c^2 \rangle$ is the mean-square speed of the molecules. Use this relation to show that the mean kinetic energy $\langle E_K \rangle$ of a molecule is $\langle E_K \rangle = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
A cylinder contains $17\,\text{g}$ of oxygen gas at a temperature of $12^{\circ}\text{C}$. The mass of $1.0\,\text{mol}$ of oxygen gas is $32\,\text{g}$. Oxygen may be treated as an ideal gas. Calculate, for the oxygen gas in the cylinder,
the mean kinetic energy for one molecule.
the total number of molecules.
the overall internal energy.