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 a 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 $9300\,\text{m s}^{-1}$. A molecule of the gas has mass $3.34 \times 10^{-27}\,\text{kg}$. Find, to three significant figures, the temperature of the star’s surface.
The radiant flux intensity from the star in (b) is $2.52 \times 10^{-8}\,\text{W m}^{-2}$ as measured at a distance of $4.16 \times 10^{16}\,\text{m}$ from the star. Calculate the luminosity of the star. Include a unit in your answer.
Find the radius of the star.
The gas on a star’s surface is under extremely high pressure. Using the basic assumptions of the kinetic theory, suggest why a gas at the star’s surface is, in practice, unlikely to act as an ideal gas.