How to Determine Heat Capacity in a Hard-Sphere Gas Simulation?

[adriplay]

I have a simulation with a bunch of particles with volume bouncing around in a box with no interaction between them, a hard-sphere gas. Initially, they all have the same momentum |p|=√(2⋅m⋅2/3⋅k⋅T) to have the average kinetic energy 3/2⋅k⋅T.

I'm asked to add a constant energy flux to the system (I solved it with a for statement that adds a little p contribution to every particle for each iteration) and to calculate the heat capacity at constant volume c_v.

As c_v is the partial derivative of <E> respect T I want to try plotting the average energy respect T but how I get the T value? I'm doing it right if I consider kT= <E>⋅2/3 knowing that I'm in an ideal approximation? How I could make it work for and interacting gas like Lennard-Jones?

 

[Andrew Mason]

I have a simulation with a bunch of particles with volume bouncing around in a box with no interaction between them, a hard-sphere gas. Initially, they all have the same momentum |p|=√(2⋅m⋅2/3⋅k⋅T) to have the average kinetic energy 3/2⋅k⋅T.

I'm asked to add a constant energy flux to the system (I solved it with a for statement that adds a little p contribution to every particle for each iteration) and to calculate the heat capacity at constant volume c_v.

As c_v is the partial derivative of <E> respect T I want to try plotting the average energy respect T but how I get the T value? I'm doing it right if I consider kT= <E>⋅2/3 knowing that I'm in an ideal approximation? How I could make it work for and interacting gas like Lennard-Jones?

Welcome to PF adriplay!

The average energy per degree of freedom per particle is kT/2. So the average energy per particle associated with the 3 translational degrees of freedom is 3kT/2.

C_v = kT/2 x the total number of degrees of freedom. In order to determine the C_v of the system of particles you have to determine the total number of degrees of freedom of the particles in the system.

Since the particles are hard spheres with a finite volume, how many degrees of rotational freedom would they have?

To find the temperature change, once you get the DOF and $C_v$, use $C_v = \frac{\Delta U}{\Delta T}$ where $\Delta U$ is the energy added to the system.
AM