Reversible and Irreversible Processes

The Core Idea: Why Some Processes Can Be Undone and Others Cannot

In thermodynamics, a process is the path a system takes from one equilibrium state to another. But not all paths are equal. Some can be reversed so perfectly that both the system and its surroundings return to their exact starting points, leaving no trace of the change. Others cannot — they leave a permanent mark on the universe.

This distinction is the foundation of the second law of thermodynamics. A reversible process is an idealisation: it happens so slowly that the system is always infinitesimally close to equilibrium. An irreversible process is the real-world counterpart — it happens at a finite rate, involves friction, turbulence, or other dissipative effects, and once it occurs, you cannot undo it without changing something else.

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What Makes a Process Reversible?

A process is reversible if the system and its surroundings can be restored to their initial states by exactly reversing the process, with no net change in the universe. This requires two conditions:

1. Quasi-static — the process must be carried out infinitely slowly, so the system passes through a continuous sequence of equilibrium states.
2. No dissipative forces — there must be no friction, viscosity, inelastic collisions, or any other effect that converts mechanical energy into heat irreversibly.

When these hold, the direction of the process can be reversed at any point by an infinitesimal change in the external conditions. For example, if you compress a gas by moving a piston infinitesimally slowly and without friction, you can reverse the motion by an equally tiny change in the external pressure, and the gas will expand back along the same path.

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What Makes a Process Irreversible?

An irreversible process is one that cannot be reversed without leaving a net change in the universe. The textbook lists several characteristic causes:

• Finite gradients — temperature, pressure, or concentration differences drive the process at a finite rate. Heat flows from hot to cold spontaneously, but to reverse that flow you would need to do work (e.g., in a refrigerator).
• Friction — kinetic friction converts mechanical work into heat. That heat can never be completely converted back into the original mechanical work.
• Free expansion — when a gas expands into a vacuum, it does no work and its temperature remains constant (for an ideal gas). To compress it back, you must do work, and that work appears as heat that must be rejected to the surroundings.
• Mixing of different substances — when two different gases mix, the process is irreversible. Separating them again would require work.
• Chemical reactions — most chemical reactions are irreversible; the products cannot spontaneously revert to reactants.
• Hysteresis — in magnetic or elastic materials, the energy lost in a cycle (the area of the hysteresis loop) is dissipated as heat and cannot be recovered.

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The Piston-and-Gas Example: Reversible vs. Irreversible Compression

The textbook uses a concrete example to make the idea clear. Consider a gas in a cylinder fitted with a frictionless piston. The piston is loaded with a pile of sand. The external pressure on the gas equals the weight of the sand divided by the piston area.

Reversible compression: Remove one grain of sand at a time. Each removal reduces the external pressure by an infinitesimal amount. The gas expands infinitesimally to equalise the pressure. The process is a continuous sequence of equilibrium states. To reverse it, add the grains back one by one — the gas compresses along the same path.

Irreversible compression: Remove a large number of sand grains at once. The external pressure drops suddenly. The gas expands rapidly, overshoots its equilibrium, and then oscillates before settling. During this process, the gas is not in equilibrium — there are pressure and temperature gradients inside. The work done by the gas is less than the work that would be required to compress it back along the same path. The difference is dissipated as heat.

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The Central Result: Work in Reversible vs. Irreversible Processes

For a gas expanding or being compressed, the work done depends on the path. The textbook derives a key inequality:

In words: a reversible expansion does the maximum possible work on the surroundings. A reversible compression requires the minimum possible work from the surroundings. Any irreversibility reduces the work output (for expansion) or increases the work input (for compression).

›Proof

Proof for expansion: Consider a gas expanding from volume $V_1$ to $V_2$. In a reversible expansion, the external pressure $P_{\text{ext}}$ is always infinitesimally less than the gas pressure $P$, so $P_{\text{ext}} \approx P$. The work done by the gas is:

$W_{\text{rev}} = \int_{V_1}^{V_2} P_{\text{ext}} \, dV \approx \int_{V_1}^{V_2} P \, dV$ …