KAHIBARO
Table of Contents
Idealized reversibility and real change
In thermodynamics, a process is a change of state of a system. Some processes are idealized as reversible, while real processes are usually irreversible. This distinction is very important because it tells us whether a process can be undone without leaving any net change in the system and its surroundings.
A reversible process is an ideal process that can be reversed by an infinitesimally small change in conditions. During such a process, the system passes through a continuous sequence of equilibrium states. If the direction is reversed, both the system and the surroundings return exactly to their initial states.
An irreversible process is any real process that cannot be completely undone in this perfect way. If we try to reverse it, some net change remains in the surroundings, in the system, or in both.
A reversible process is an ideal limit, not a perfectly realizable real process.
An irreversible process is the natural form of real processes.
Reversible means the system and surroundings can both be restored exactly.
What makes a process reversible
For a process to be reversible, it must happen extremely slowly, so that the system remains very close to thermodynamic equilibrium at every moment. Also, there must be no dissipative effects such as friction, viscosity, turbulence, electrical resistance, or unrestrained expansion.
A classic example is the very slow expansion of a gas in a cylinder with a frictionless piston. If the external pressure differs from the gas pressure by only an infinitesimal amount, the piston moves slowly and the process can be treated as reversible.
If the pressure difference is finite, the gas expands suddenly, the system is not in equilibrium during the change, and the process becomes irreversible.
Mechanical picture
A reversible compression or expansion can be imagined as a piston that moves so slowly that the gas pressure inside is always almost equal to the external pressure.
In the left case, the piston moves slowly and can be reversed with an extremely small change in pressure. In the right case, the motion is sudden, so the process is irreversible.
Common examples of irreversible processes
Many familiar processes are irreversible. Heat flowing from a hot object to a cold one is irreversible. Gas freely expanding into a vacuum is irreversible. Frictional sliding is irreversible. Mixing of two gases is irreversible. Electric current through a resistor is irreversible.
These processes all involve dissipation or spontaneous change in one preferred direction.
The following table compares typical cases.
| Process | Reversible or irreversible | Main reason |
|---|---|---|
| Infinitely slow compression of gas | Reversible, idealized | System stays near equilibrium |
| Free expansion into vacuum | Irreversible | No opposing pressure, no equilibrium path |
| Heat transfer across finite temperature difference | Irreversible | Spontaneous heat flow |
| Frictionless quasistatic expansion | Reversible, idealized | No dissipation |
| Motion with friction | Irreversible | Mechanical energy dissipated |
| Mixing of gases | Irreversible | Cannot be exactly undone naturally |
Heat transfer and reversibility
Heat transfer is reversible only in the ideal case where it occurs across an infinitesimal temperature difference. If heat flows from temperature $T_h$ to $T_c$ with $T_h > T_c$ by a finite difference, the process is irreversible.
This means that a reversible heat transfer requires the temperatures of the system and surroundings to differ by only an infinitesimal amount at each step.
Heat transfer is reversible only when it occurs through an infinitesimal temperature difference.
Heat transfer through a finite temperature difference is irreversible.
Work in reversible and irreversible processes
For a gas expanding from one volume to another, the work depends on how the process happens. In a reversible process, the pressure is well defined at every stage, so the work is
$$
W_{\text{rev}} = \int P \, dV
$$
where $P$ is the pressure of the gas during the reversible path.
For an irreversible expansion against a constant external pressure $P_{\text{ext}}$,
$$
W_{\text{irr}} = P_{\text{ext}} (V_f - V_i)
$$
For the same initial and final states, reversible expansion gives the maximum work done by the system. Reversible compression requires the minimum work done on the system.
For the same initial and final states, reversible expansion gives maximum work by the system.
Reversible compression requires minimum work on the system.
Reversible paths and state changes
A thermodynamic state is determined by state variables such as pressure, volume, and temperature. The change in state can be the same even if the path is different. Reversible and irreversible processes may connect the same initial and final states, but they are not the same path.
This is why quantities like work and heat depend on the path, while state variables depend only on the endpoints.
Quasistatic is not always reversible
A quasistatic process is one that happens very slowly, so the system passes through states close to equilibrium. This is necessary for reversibility, but it is not sufficient.
If friction is present, the process may still be slow, but it is not reversible. So every reversible process is quasistatic, but not every quasistatic process is reversible.
| Property | Quasistatic | Reversible |
|---|---|---|
| Very slow change | Yes | Yes |
| Near equilibrium states | Yes | Yes |
| No dissipative effects required | No | Yes |
| Perfectly restorable system and surroundings | No | Yes |
Entropy and irreversibility
The deepest thermodynamic distinction between reversible and irreversible processes is expressed through entropy. In a reversible process, the total entropy of the universe does not increase. In an irreversible process, the total entropy increases.
If we define the universe as system plus surroundings, then
$$
\Delta S_{\text{universe}} = 0 \quad \text{for a reversible process}
$$
and
$$
\Delta S_{\text{universe}} > 0 \quad \text{for an irreversible process}
$$
This gives a practical criterion for direction in natural processes.
Entropy criterion:
$$
\Delta S_{\text{universe}} = 0 \quad \text{reversible}
$$
$$
\Delta S_{\text{universe}} > 0 \quad \text{irreversible}
$$
Why reversibility matters
Reversible processes are useful because they define ideal limits. They show the maximum efficiency a heat engine could have and the minimum work needed in many thermodynamic operations. Real devices always perform worse because real processes are irreversible.
So, reversible processes are not common in nature, but they are essential as reference models. Irreversible processes describe the actual behavior of physical systems.
Final perspective
A reversible process is a perfect thermodynamic ideal, slow, balanced, and free from dissipation. An irreversible process is the realistic process we observe in nature, involving finite gradients, friction, mixing, or spontaneous flow.
Learning this distinction helps us understand why real machines waste energy, why natural processes have a preferred direction, and why equilibrium is so important in thermodynamics.