Total energy of a star in terms of average temp.

[JDStupi]

Homework Statement

The problem I am doing is problem 1.55 in Schroeders Intro to Thermal Physics. Unfortunately, I have to come here for help a lot because the office hourse are not until after the homework is due...In any case, the first part of the question was to show that the potential energey of a system of two mutually gravitating particles in a circular orbit is equal to -2Kinetic of the system. From here it asks me what would happen to the average total kinetic energy of the system if you add energy to the system and wait for it to equilibriate.
I wouldl ike some help with how to think about this

Also, the other part I am on says "A star can be modeled as a gas of particles that interact with each other only gravitationally. According to the equipartition theroem, the average kinetic energy of the particled in such a star should be 3/2kt, where T is the average temperature. Express the total energy of a star in terms of its avg temp and calculate the heat capacity"




All I have is this, but It just seems wrong to me and I am not sure if I am going in the right direction
:
Because we have established that the U=(-2)K where U is the potential energy and K=3/2KT by the equipartition theorem We get:

(Letting P equal potential because later U comes in as total)

P=(-2)(3/2KT)=(-3KT). The total energy, then would be the sum of the potential and the kinetic which would be (K+P)=(3/2kT-3kT)=-3/2kT.

This has the unfortunate consequence of having a negative total energy, that is assuming the temperature is positive, which on a Kelvin scale it must be, therefore I believe I did something wrong and do not know how to proceed.

Because we already included the gravitational potential into the calculations the heat capacity C=Q/ΔT=(ΔU-W)/ΔT)=(ΔU)/(ΔT)=(dU/dT)=-3/2k

 

[member 553083]

Homework Equations U=(-2)K K=3/2KTThe Attempt at a SolutionI have tried to express the total energy of the star in terms of its average temperature and calculate the heat capacity, but it is not coming out correctly.