Helium stars are really interesting thermodynamic systems because they can be modeled as isolated spheres of N ideal gas particles held together by gravity. Considering this, prove that for such a system, the gravitational potential energy is -2 times its total kinetic energy (you may prove it by considering 2 identical particles orbiting around their center of mass, see picture.) express the total energy of the star in terms of its average temperature. determine an expression for the star’s heat capacity. calculate the entropy in terms of average temperature. calculate the entropy as a function of total energy, U, then plot S vs. U. Explain your observations: i.e. what is happening with temperature? What other systems exhibit this behavior?

Helium stars are really interesting thermodynamic systems because they can be modeled as isolated spheres of N ideal gas particles held together by gravity. Considering this, prove that for such a system, the gravitational potential energy is -2 times its total kinetic energy (you may prove it by considering 2 identical particles orbiting around their center of mass, see picture.) express the total energy of the star in terms of its average temperature. determine an expression for the star’s heat capacity. calculate the entropy in terms of average temperature. calculate the entropy as a function of total energy, U, then plot S vs. U. Explain your observations: i.e. what is happening with temperature? What other systems exhibit this behavior?