The evolution of a 2-dimensional ideal gas in a constant gravitational field toward the state of equilibrium.

Kostas Papamichalis Dr of Theoretical Physics

The theoretical model - Features of the simulation - Activities (pdf-file)

The purpose of the application is to study "experimentally" the evolution of a 2-dimensional ideal gas towards its equilibrium state. The gas is under the action of a constant vertical gravitational field, which causes that the y-position-distribution of the gas to converge to an exponential-like form. This form is sometimes called "exponential atmosphere".

In the sim-window you can see the motion and the interactions of the gas-particles. One of the particles has been colored red and its trajectory is visible to the user. At time t=0, you can see the vectors of the particles' velocities corresponding to the initial velocity distribution. The velocities of the particles in the initial state have random directions and the same magnitude v_in. The initial position-distribution is ubiform and its explicit form is determined by the user. The form of the position-distribution is changing with time and converges to the exponential equilibrium distribution.

In the upper graph-window you can see how the position-distribution of the gas is changing with time, because of the particles' interactions and the action of the gravitational field.
The lower graph depicts the variation of the mean kinetic (red curve) and the mean potential energy (blue curve) in real time.
It must be noticed that the graphs are completely "experimental" in the environment of the application: they are composed by measurements of the particles-positions at a sequence of specified time-moments. The motion of the particles is determined by the Newton laws, their interactions and their initial states.
The number of the particles is N=400. The user can choose the common initial kinetic energy of the particles.
The energy is conserved in each p-p interaction, as well between the particles and the boundaries of the vertical strip. Furthermore, the user controls two more parameters:
The "p-p control factor" s of the interaction (see the attached file).
The intensity of the gravitational field g.

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