(a)[2]
State the meaning of an ideal gas.
(b)
An ideal gas has a pressure of $1.6 \times 10^5\,\text{Pa}$ and a density of $1.9\,\text{kg m}^{-3}$.
(b(i))[3]
Show that the root-mean-square (r.m.s.) speed of molecules of this gas is about $500\,\text{m s}^{-1}$.
(b(ii))[2]
One molecule of the gas has a mass of $4.7 \times 10^{-26}\,\text{kg}$. Determine the thermodynamic temperature of the gas.
(c)[3]
Calculate the internal energy $U$ of $6.0\,\text{mol}$ of the gas in (b), and explain how you reached your answer.