This JS application allows you to simulate the evolution of a monoatomic perfect gas, contained in a cubic volume, throughout successive states of themodynamic equilibrium, to show this evolution by a graphic animation, to produce the graphs of the relations between volume, pressure and temperature, to produce the tables of the values of some parameters related to the represented states.

The functions of the application can be selected from the main menu:

• Transformations and Cycles
• Graphs
• Tables

The user can modify the parameters of the simulations by selecting proper values in the following selectors:

• number of particles
• mass of a particle
• minimum temperature
• maximum temperature
• initial edge of the cube
• final edge of the cube
• number of steps
• number of frames per step
• duration of a frame
• graphic dimension of a particle (1 ≤ d ≤ 5)

The user can set on or set off the graphic animation.

volume

In these simulations the volume occupied by the gas is that of a cube with variable edge.

In the animations the cube is seen from the front so it appears as a square. The user can write in proper input fields the initial side and the final side.

The measures of the side are expressed in millimeters: in the graphics every millimeter is represented by a pixel.

In the output fields and in the tables the volume is measured in litres.

perfect (or ideal) gas

In these simulations the gas is a system formed by a fixed number of particles which are thinked to be punctiform and having only translational kinetic energy.

Every particle has its own position and its own velocity. All the particles have identical mass.

The initial positions of the particles are randomly generated within the volume.

The velocities are generated with random directions. The squares of their values are disposed with gaussian distribution around a mean value depending on the initial temperature of the system. Because of this random initialization, the initial temperature of the system, related to its mean molecular kinetic energy, is often near but does not coincide with that written in the input field init. temp.

In the simulations, to obtain perceptible values of the pressure using few slow particles, the masses of the particles must be enormous with respect to the realistic ones. They can be only multiple values of 10¹⁰ u.m.a. So the number in the input field molecular mass must represent this multiple.

At the same temperature, the greater is the mass of a particle, the slower it is.

A particle do not interact with other particles. It interact only with the walls of the container by elastic collisions. In the simulations the pressure of the gas is measured calculating the variation of the momentum of every particle in these collisions.

pressure

The pressure of the gas on the walls is evaluated by the average variation of the momentum in the unit of time.

To produce graphs with visible values of the pressure, the unit of measure of the pressure in the output fields is the decielectronvolt per litre (deV/l).

Transformations

This applet simulates the thermodynamic transformations starting from the initial state and reaching the final one through a prefixed number of intermediate stationary states. The user must write this number in the input field steps.
Every state of the system is analyzed for a duration specified by the inputted number of frames.
The permanence of the representation of every frame of the graphic animations is fixed, in milliseconds, in the field delay.

The applet allows simulations of the following transformations.

• Isothermal.

  Given the initial temperature, the initial and the final side, the system makes the programmed number of steps, starting from the initial volume to the final one keeping its temperature constant.
  In the isothermal processes volume and pressure are inversely proportional (Boyle's low). The diagram of an isothermal transformation in the VP plane is a branch of an equilateral hyperbola.

• Isochoric

  Given the initial side, the initial and the final temperature, the system makes the programmed number of steps keeping its volume constant.
  In the isochoric processes the pressure and the absolute temperature are directly proportional. The diagram of an isochoric transformation in the TP plane is a segment of a straight line.

• Isobaric

  Given the initial and the final side and the initial temperature, the system makes the programmed number of steps keeping its pressure constant.
  In the isobaric processes the volume and the absolute temperature are directly proportional. The diagram of an isobaric transformation in the TV plane is a segment of a straight line.

• Adiabatic

  Given the initial and the final side and the initial temperature, the system makes the programmed number of steps without exchange of heat with the environment.
  In the adiabatic processes the pressure is inversely proportional to a power of the volume in which the exponent is γ (gamma) i.e. the ratio between the molar specific heat at constant pressure (c_p) and the molar specific heat at constant volume (c_v). For an ideal monoatomic gas: γ=5/3. The diagram of an adiabatic transformation in the VP plane is a branch of an exponential curve.

• Generic

  Given the initial and the final side and the initial and final temperature, the system makes the programmed number of steps in a way not referable to any of the previous transformations.
  The final temperature isn't the effective temperature finally reached by the system. Here it is only a way to determine the amount of heat exchanged during the transformation.

Cycles

A series of transformations ending when the system returns to its initial state is called thermodynamic cycle.
This applet allows simulations of the following cycles.

• Carnot

  By an isothermal expansion the system goes from the initial to the final volume;
  by an adiabatic expansion the system reaches the final temperature, lower than initial one;
  by an isothermal compression and a following adiabatic compression the system returns to its initial state.

  Input the initial and final side and the initial and the final temperature.
  If the final temperature is higher than the initial one, the software makes an exchange. So happens if the initial side is greater than the final one.

• Stirling

  By an isothermal expansion the system goes from the initial to the final volume;
  by an isochoric cooling the system reaches the final temperature, lower than initial one;
  by an isothermal compression and a following isochoric heating the system returns to its initial state.

  Input the initial and final side and the initial and the final temperature.
  If the final temperature is higher than the initial one, the software makes an exchange. So happens if the initial side is greater than the final one.

• Otto

  By an adiabatic compression the system goes from the initial to the final volume;
  by an isochoric heating the system reaches the final temperature, higher than initial one;
  by an adiabatic expansion up to the initial volume and a following isochoric cooling the system reaches its initial state.

  Input the initial and final side and the initial and the final temperature.
  If the final temperature is lower than the initial one, the software makes an exchange. The final temperature must be much higher than the initial one. The initial side must be greater than the final one. Otherwise they are exchanged.

• Diesel

  By an adiabatic compression the system goes from the initial to the final volume, which must be smaller than the initial one;
  by an isobaric heating the system reaches the final temperature, which must be higher than the initial one;
  by an adiabatic expansion up to the initial volume and an isochoric cooling the system returns to its initial state.
  If the final temperature is lower than the initial one, the software makes an exchange. The initial side must be greater than the final one. Otherwise they are exchanged.

Every transformation composing a cycle is divided in a number of steps corresponding to the number written in the input field steps.

The last two cycles require a big difference between T_max and T_min.

Graphs

The function Graph of the main menu can produce three diagrams for every simulated transformation or cycle:

• Volume/Pressure;
• Temperature/Volume;
• Temperature/Pressure.

The measure units used on the axes are the same used within the tables.

Tables

At every step of the simulated transformations or cycles, the applet writes the values of the following quantities:

• Volume (litre);
• Pressure (decielectronvolt/litre);
• Temperature (hKelvin);
• Energy variation (electronvolt);
• Work (electronvolt);
• Heat exchanged (electronvolt);
• Entropy variation: (electronvolt/Kelvin);