Help with the Virial Theorem please

In summary: M sub is the mass of the subatomic particles, and r sub is the radius of the sphere. So if I have a system of particles that have potential energy (omega) and I want to know the kinetic energy (KE), I can use the equation 2KE + PE = 0. In this equation, KE is the energy of the particles, and PE is the energy of the potential.
  • #1
Alfie114
3
0
TL;DR Summary
I have a question about the virial theorem as applied to a cluster of stars.
Anyone able to help if I provide you with more details?
 
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  • #2
:welcome:

You might need to provide a bit more detail about your question.
 
  • #3
OK we have a star cluster (the system) which is made up from stars (total mass M sub *) and gas (total mass M sub g). The stars and gas are all distributed as spheres of constant density and a finite radius r sub c.

The total mass of the stars and the gas is different but we can assume that M sub g = f*M sub *

If the system is unrotating and in equilibrium how do we calculate the kinetic energy in terms of r sub c, f and M sub *?

We can take 2KE + PE = 0 where KE = (-3/5) (GM^2/R) and PE = (3kT/2)*n where n is the total number of particles = (M/mu*m sub H) where mu=1 and m sub H is the mass of a hydrogen atom.
 
  • #4
Alfie114 said:
OK we have a star cluster (the system) which is made up from stars (total mass M sub *) and gas (total mass M sub g). The stars and gas are all distributed as spheres of constant density and a finite radius r sub c.

The total mass of the stars and the gas is different but we can assume that M sub g = f*M sub *

If the system is unrotating and in equilibrium how do we calculate the kinetic energy in terms of r sub c, f and M sub *?

We can take 2KE + PE = 0 where KE = (-3/5) (GM^2/R) and PE = (3kT/2)*n where n is the total number of particles = (M/mu*m sub H) where mu=1 and m sub H is the mass of a hydrogen atom.
You need to use math latex notation. Its hard to understand your equations like this.
 
  • #5
Ok I've got these where omega is the potential energy
1575636887584.png
1575636809181.png
 

1. What is the Virial Theorem?

The Virial Theorem is a mathematical relationship between the kinetic and potential energies of a system, which can be used to analyze the stability and equilibrium of a system.

2. How is the Virial Theorem used in science?

The Virial Theorem is used in various fields of science, such as astrophysics, thermodynamics, and quantum mechanics, to analyze the behavior and stability of systems.

3. What is the significance of the Virial Theorem?

The Virial Theorem provides a way to understand the behavior of complex systems by relating their kinetic and potential energies. It also allows for the prediction of system stability and equilibrium.

4. What is the formula for the Virial Theorem?

The formula for the Virial Theorem is: 2 = -, where represents the average kinetic energy and represents the average potential energy of the system.

5. How is the Virial Theorem related to the law of conservation of energy?

The Virial Theorem is derived from the law of conservation of energy, as it states that the total energy of a system remains constant. It is a mathematical representation of the law of conservation of energy for systems with both kinetic and potential energies.

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