# Linear Potential and Thermal Equilibrium

1. Jan 22, 2012

### JonathanT

"Linear" Potential and Thermal Equilibrium

1. The problem statement, all variables and given/known data

Consider a classical particle moving back and forth along the x-axis while restrained by a "Linear" potential V(x) = b|x|. If the particle is in thermal equilibrium with the environment at temperature T, calculate the mean value of the potential energy b|x|.

2. Relevant equations

Equipartition Theorem: Each term in the energy proportional to the square of a velocity or a coordinate contributes $\frac{1}{2}$kT to the mean energy at thermal equilibrium.

Where k is the Boltzmann Constant
T is the Temperature in Kelvin

3. The attempt at a solution

Basically I'm just confused by the question. Maybe its the wording or I'm oversimplifying it.

If I used the Equipartition Theorem for the mean potential energy in the system the answer would just be $\frac{1}{2}$kT right? Seeing as the system only has 1 "degree of freedom." Obviously I'm missing the point of the equation given in the problem. V(x) = b|x|. Or how to manipulate it in order to get a logical conclusion rather then just stating the answer.