Syllabus Points — Ideal Gases

15.1 The mole

1. understand that amount of substance is an SI base quantity with the base unit mol
2. use molar quantities where one mole of any substance is the amount containing a number of particles of that substance equal to the Avogadro constant $N_A$

15.2 Equation of state

1. understand that a gas obeying $pV \propto T$, where $T$ is the thermodynamic temperature, is known as an ideal gas
2. recall and use the equation of state for an ideal gas expressed as $pV = nRT$, where $n$ = amount of substance (number of moles) and as $pV = NkT$, where $N$ = number of molecules
3. recall that the Boltzmann constant $k$ is given by $k = R/N_A$

15.3 Kinetic theory of gases

1. state the basic assumptions of the kinetic theory of gases
2. explain how molecular movement causes the pressure exerted by a gas and derive and use the relationship $pV = \frac13 Nm\langle c^2\rangle$, where $\langle c^2\rangle$ is the mean-square speed (a simple model considering one-dimensional collisions and then extending to three dimensions using $\frac13 \langle c^2\rangle = \langle c_x^2\rangle$ is sufficient)
3. understand that the root-mean-square speed $c_{\text{r.m.s.}}$ is given by $\sqrt{\langle c^2\rangle}$
4. compare $pV = \frac13 Nm\langle c^2\rangle$ with $pV = NkT$ to deduce that the average translational kinetic energy of a molecule is $\frac32 kT$, and recall and use this expression