Free (Joule) Expansion of a Gas: A Thermodynamic Classic |…

What Free Expansion Is

Free (Joule) expansion is a process where a gas expands into an evacuated space without doing any external work. This occurs when a partition separating two compartments of a container is removed, allowing the gas to fill both sides of the container.

In this 2D simulation, you observe how the gas molecules rush from one side of the container to occupy the entire available volume, illustrating the spontaneous nature of such expansions.

Why It Happens

The expansion happens because the gas molecules have more space to move around. In statistical mechanics, this leads to an increase in entropy since there are now more microstates available for the system.

The process is adiabatic (no heat exchange) and quasi-static (the partition's removal is instantaneous), making it a perfect example of how internal energy depends solely on temperature.

live demo · related simulation● LIVE

Key Observations

In the simulation, you can observe that the mean molecular speed remains constant during the expansion. This is because no external work is done by or to the gas, and thus its kinetic energy (and hence temperature) does not change.

The density profile shows a rapid decrease in concentration on one side of the partition followed by an increase as the gas spreads out evenly across both sides.

Real-World Applications

Free expansion is relevant in various real-world scenarios, such as in thermometers and in understanding the behavior of gases in engines or refrigeration systems.

It also helps in explaining phenomena like the sudden increase in entropy when a gas expands into a vacuum.

Frequently asked questions

How does free expansion differ from isothermal expansion?

In free expansion, no work is done by or on the gas and it occurs instantaneously. In contrast, isothermal expansion involves heat transfer to maintain constant temperature.

Why does mean molecular speed stay constant during free expansion?

The mean molecular speed remains unchanged because there's no external force acting on the gas molecules during this process, and thus their kinetic energy (and therefore temperature) is conserved.

Can we reverse a free expansion process?

Reversing a free expansion would require work to be done against the internal pressure of the gas, which is not possible without an external mechanism or additional heat input.

What does the entropy increase during free expansion signify?

The entropy increase signifies that the system has become more disordered. The gas molecules now have a greater number of accessible microstates as they spread out into the available volume.

Try it live

Everything above runs in your browser — open Free (Joule) Expansion of a Gas — 2D and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Free (Joule) Expansion of a Gas — 2D simulation