9702/41/O/N/23: (a) The product pV for an ideal gas is given by pV =1/3Nmc^2 where p is the pressure of the gas and V is the volume of the gas.
(i) State the meaning of the symbols N, m and〈c2〉 in this equation.
(ii) Use the equation of state for an ideal gas to show that the average translational kinetic energy EK of a molecule of the gas at thermodynamic temperature T is given by EK = 3/2 kT.
(b) The surface of a star consists mainly of a gas that may be assumed to be ideal. The molecules of the gas have a root-mean-square (r.m.s.) speed of 9300ms-1. The mass of a molecule of the gas is 3.34 × 10-27 kg. Determine, to three significant figures, the temperature of the surface of the star.
(c) The radiant flux intensity of the radiation from the star in (b) is 2.52 × 10-8Wm-2 when observed at a distance of 4.16 × 10^16m from the star.
(i) Calculate the luminosity of the star. Give a unit with your answer.
(ii) Determine the radius of the star.
(d) The gas at the surface of a star has a very high pressure. Use the basic assumptions of the kinetic theory to suggest why, in practice, a gas at the
surface of a star is unlikely to behave as an ideal gas.
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