A process is reversible if, after it has been carried out, it is possible to restore both the system and its entire surroundings to exactly the same states they were in before the process. If the system and its surroundings cannot return to their initial states at the end of the reversed process, this process is an irreversible process.

A system can be restored to its initial state following a process, regardless if the process is reversible or not. If the surroundings can also be restored to its initial state, the process is reversible. Otherwise, the process is irreversible.

Reversible process does not occur in nature. It is the idealization of actual process and serves as an idealized model to which actual process can be compared.

The factors that cause a process to be irreversible are called irreversibilities. They include:

• heat transfers through a finite temperature difference
• unrestrained expansion of a gas
• mixing of two gases
• friction
• electric current flow through a resistance
• inelastic deformation
• chemical reactions

The process is irreversible if any of these effects present.

When a process is carried out, irreversibilities can be found within the system as well as in the system's surroundings. A process is called internally reversible if the system can be restored through exactly the same equilibrium states which the system goes through. No irreversibilities occur within the boundaries of the system as it goes through the process.

If no irreversibilities occur outside the system boundaries during the process, the process is called externally reversible.

A process is called totally reversible, or reversible, if it is both internally and externally reversible.

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The Carnot Cycle (1-2): Reversible Isothermal Expansion

The Carnot Cycle (2-3): Reversible Adiabatic Expansion

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The Carnot Cycle (3-4): Reversible Isothermal Compression

Carnot Cycle (4-1):
Reversible Adiabatic Compression

Heat engine operates on a cycle. The efficiency of heat engine depends on how the individual processes are executed. The most efficient cycles are reversible cycles, that is, the processes that make up the cycle are all reversible processes.

Reversible cycles cannot be achieved in practice. However, they provide the upper limits on the performance of real cycles.

Carnot cycle is one of the best-known reversible cycles. The Carnot cycle is composed of four reversible processes. Consider an adiabaticpiston-cylinder device that contains gas. The four reversible processes that make up the Carnot cycle are as follows:

• Reversible Isothermal Expansion (process 1-2):
  Heat transfer between the heat source and the cylinder occurs with an infinitesimal temperature difference. Hence, it is a reversible heat transfer process. Gas in the cylinder expands slowly, does work to its surroundings, and remains at a constant temperature T_H. The total amount of heat transferred to the gas during this process is Q_H.
• Reversible adiabatic expansion (process 2-3):
  The heat source is removed, and the gas expands in an adiabatic manner. Gas in the cylinder continues to expand slowly, do work to its surroundings till the temperature of the gas drops from T_H to T_L. Assuming the piston moves frictionless and the process to be quasi-equilibrium, the process is reversible as well as adiabatic.
• Reversible isothermal compression (process 3-4):
  The cylinder is brought into contact with a heat sink at temperature T_L. The piston is pushed by an external force and which does work on the gas. During the compression, the gas temperature maintains at T_L and the process is a reversible heat transfer process. The total amount of heat rejected to the heat sink from the gas during this process is Q_L.
• Reversible adiabatic compression (process 4-1):
  The heat sink is removed and the gas is compressed in an adiabatic manner. Gas in the cylinder continues to be compressed slowly, accepting work from its surroundings till the temperature of the gas rises from T_L to T_H. The gas returns to its initial state, which completes the cycle.

If the processes that make up the cycle of the heat engine are all reversible processes, the heat engine is a reversible heat engine. Otherwise, it is an irreversible heat engine. In practice, all heat engines are irreversible since no reversible process exists in nature.

The Carnot Principles are conclusions of the second law of thermodynamics. They are expressed as follows:

• The efficiency of an irreversible heat engine is always less than that of a reversible one operating between the same two reservoirs.
• The efficiencies of all reversible heat engines operating between the same two reservoirs are the same.