For an ideal gas, the product $pV$ is given by $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $p$ is the pressure of the gas and $V$ is the volume of the gas. State what the symbols $N$, $m$ and $\langle c^2 \rangle$ mean in this equation.
Use the ideal gas equation of state to show that the average translational kinetic energy $E_K$ of one molecule of the gas at thermodynamic temperature $T$ is $E_K = \frac{3}{2}kT$.
A star’s surface is made mainly of a gas that can be treated as ideal. The gas molecules have a root-mean-square (r.m.s.) speed of $9300\,\text{m s}^{-1}$. The mass of one gas molecule is $3.34 \times 10^{-27}\,\text{kg}$. Determine, to three significant figures, the temperature at the star’s surface.
The radiant flux intensity of the radiation from the star in (b) is $2.52 \times 10^{-8}\,\text{W m}^{-2}$ when it is measured at a distance of $4.16 \times 10^{16}\,\text{m}$ from the star. Calculate the luminosity of the star. Give a unit with your answer.
Find the radius of the star.
The gas at a star’s surface is under very high pressure. Use the main assumptions of kinetic theory to suggest why, in practice, a gas at a star’s surface is unlikely to behave as an ideal gas.