(a(i))[3]
State what each symbol in this equation represents: $p$, $V$, $N$, $k$, $T$.
(a(ii))[2]
Using the equation of state, derive an expression for the mean translational kinetic energy $E_K$ of a particle in the gas in terms of some or all of $N$, $k$ and $T$.
(b)[2]
A hydrogen gas molecule contains two hydrogen atoms, each with nucleon number 1. An oxygen gas molecule contains two oxygen atoms, each with nucleon number 16. Suppose hydrogen and oxygen both act as ideal gases. A sample of hydrogen gas is at the same temperature as a sample of oxygen gas. For these two samples, find the ratio $\dfrac{\text{root-mean-square (r.m.s.) speed of hydrogen molecules}}{\text{root-mean-square (r.m.s.) speed of oxygen molecules}}$.