# Virial Theorem and Energy of a Two-Body System

1. Jan 2, 2014

### torq123

Hi all,

I want to make sure I am understanding this correctly.

Say we have two identical particles orbiting (in circles) about their center of mass.

We know that the average potential energy is -2 times the average kinetic energy.

So the average total energy is negative the average kinetic energy.

If we add a bit of energy to this system and wait for it to equilibrate, will the average kinetic energy increase or decrease?

My thought would be that it would decrease, because since the average total energy is negative the average kinetic energy, kinetic energy would have to decrease to make the math work.

Is there a good way to understand this, physically? And did I even reach the right conclusion?

2. Jan 2, 2014

### Meir Achuz

Since E=T+V, and V=-2T, E=-T. Therefor adding energy makes T smaller.

3. Jan 2, 2014

### kittu1421

That's a correct inference drawn and what u hav mentioned here is unsophisticated definition of Virial theorem......this is put to the explanation of negative heat capacities... for bounded system as mentioned above, an addition to the energy causes a decrease in kinetic energy..and since temperature is nothing but a manifestation of K.E., with the addition of energy the temp. of system decreases as well...