One assumption of the kinetic theory of gases is that gas molecules act like hard, elastic identical spheres. State two further assumptions of the kinetic theory of gases.
From kinetic theory, the pressure $p$ multiplied by the volume $V$ of an ideal gas is shown to satisfy $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $m$ is the mass of a gas molecule.
State what the symbol $N$ represents.
State what the symbol $\langle c^2 \rangle$ means.
Use the expression to deduce that the mean kinetic energy $\langle E_K \rangle$ of a gas molecule at temperature $T$ is given by $\langle E_K \rangle = \frac{3}{2}kT$, where $k$ is a constant.
State the definition of the internal energy of a substance.
Use the equation in (b)(ii) to explain that, for an ideal gas, $\Delta U \propto \Delta T$, where $\Delta T$ is the change in temperature of the gas.