SimuLab 14: Kinetic and Potential Energies of Particles in Liquid State


Your objective is to:

Recognize the difference between a gas and a liquid in terms of the energies of the particles.

You will be able to:

Differentiate among the liquid and gas state in terms of average kinetic energy and the average potential energy of the particles.

Contrast the potential energy of a molecule in the center of a droplet with that on the edge of the droplet.

State the relationship between the trajectory of a particle and its potential energy.

Explain the release of latent heat when a gas condenses.

    1. Open SMD, select Experiment 1 in the preset experiments in Energy folder and press Start. Make sure that the Iterations between Displays are 5.

    You are visualizing 144 particles of a high-density gas. There is no exchange of energy with the surroundings (the system is thermally isolated) and thus the total energy of the system is conserved.

    2. Pause the simulation and reduce the temperature to 0.01. Press Start.

    At first the particles almost stop, but then they start to accelerate toward each other, and form little droplets. The formation of droplets is called condensation and occurs naturally in clouds.


Q3.13: Do you expect a particle in the center of a droplet to have the same or different potential energy when compared to a particle at the edge of the droplet. Explain your reasoning.

    3. In order to speed up the simulations change Iteration between Displays to 100. Press Pause and switch Display Particles by to Potential Energy and press Start.

    The temperature steadily increases until it levels out. Notice that the droplets break apart and that the color of particles in the middle of the droplets changes to yellow (i.e these particles have a relatively low potential energy).


Q3.14: When you lowered the temperature of the system to 0.01 what happened? Explain the rise in temperature you observe.


Figure 3.6: The system showing the gas near its condensation point. Little droplets of liquid form, but almost immediately break apart. The color coding indicates the potential energy. The particles in the droplets are green and yellow, indicating that they have relatively low potential energy.

    4. Switch the Graph to Energies. If mor than 50 time units elapsed, Reset the experiment and repeat step 2.

    Notice how, during the experiment, the average potential energy decreases while the average kinetic energy has increased.


Q3.15: Explain why during condensation, in a thermally isolated system, many small droplets form, but they do not coalesce to form a single dropplet.


Figure 3.7: The system is at constant temperature of T=0.4. The graph shows average kinetic energy (top line), total energy (middle line), and potential energy (bottom line), all with virtually no fluctuation. Almost all the gas condenses into liquid droplets that are in equilibrium with the surrounding gas, which is of extremely low density. Some of the particles escape from the droplets and some coalesce with them. The color coding indicates the potential energy of each particle. Note that the particles in the middle of the droplet have the lowest potential energy. The time on the graph indicates the time elapsed since the beginning of condensation, i.e., since the temperature was lowered from T=1 to T=0.4.

    5. Reset the experiment. Switch Display Particles by to Potential Energy. Switch the Graph to Energies and set the temperature to 0.4. This temperature is below the condensation point. Put the Heat Bath on and press Start. Watch the system for 200 times units.

    In order to simulate a gas-liquid transition, we must cool the system further. In order to achieve this, the latent heat of condensation that is produced must be dissipated into the larger surrounding system. This is done on the computer by putting the Heat Bath on. Now the system will exchange energy with the surroundings. See how the droplets form steadily.


Q3.16: What happens to the energies, Ek, Ep and ET of the system?

    6. Because the condensation process requires a significant amount of computer time, we recommend opening the Experiment1a file. Switch the graph to potential energies.

    This starts the experiment at the stage where almost all the particles have coalesced into large droplets (see Fig. 3.7).


Q3.17: Watch the colors of the particles in the big droplet (see Fig. 3.7). In the center they turn to orange and yellow while on the edges they remain green.

Explain why? Clue: how many neighbors do the particles in the center have compared to those on the edge?


Q3.18: Explain the changes you see in terms of potential energy of particles at the moment when a particle leaves the droplet and when it joins the droplet.

    7. Switch Display Particles by to Trajectories and press Start.

    The particles in the droplet move along curved lines, while in the gas they move along straight lines.


Q3.19: How do you explain these trajectories in terms of the potential energies of the particles?