A giant star has a radius of 200 Rsun, with core mass 0.6 Msun surrounded by an extended envelope of mass 0.2 Msun.
a.) Estimate the gravitational potential energy of the envelope.
b.) By applying Virial Theorem to the envelope, determine the thermal energy U of the gas in the envelope, and hence estimate the total energy of the envelope.
c.) Suppose that the envelope is composed entirely of ionized hydrogen. How much energy would be liberated if the gas cooled and all the protons and electrons recombined to form neutral hydrogen (the recombination of energy is 13.6 eV per atom)?