Reversible & Irreversible Thermodynamic Processes - Thermodynamics - Mechanical Engineering

Fundamental idea

In a state of thermodynamic equilibrium there are no internal gradients of mechanical, thermal or chemical potential; consequently the macroscopic properties of the system remain steady in time. If a disturbance (for example a change in external pressure, a temperature difference or a change in composition) is imposed on such a system, the system departs from its initial equilibrium and evolves toward a new equilibrium. Whether this evolution is reversible or irreversible depends on whether the process can be reversed so that both the system and its surroundings are returned exactly to their initial states through the same sequence of intermediate equilibrium states.

Illustration: gas in a piston-cylinder

Consider a simple closed system consisting of a gas confined by a frictionless piston. Initially the gas pressure equals the external pressure due to the piston weight and its temperature equals that of the surroundings; hence the system is at equilibrium (state A). If a small mass is placed on the piston, the external pressure becomes slightly larger than the gas pressure and the piston moves downward until a new equilibrium (state B) is reached. Repeating this operation with more masses in small increments moves the system through a sequence of states from A to X.

Fig. 1.5 Illustration of Reversibility of Thermodynamic Process

If each mass is removed in the reverse order and in the same incremental manner, and if at every intermediate stage the system and surroundings return through exactly the same states as in the forward process, the overall process A → X → A is reversible. If the reverse path does not coincide with the forward path, or if the surroundings are not restored to their initial condition, the process is irreversible.

Quasi-static processes and reversibility

A quasi-static process is one that proceeds infinitely slowly so that the system at each instant remains arbitrarily close to equilibrium. Quasi-staticity is necessary but not sufficient for reversibility: all reversible processes must be quasi-static, but a quasi-static process can still be irreversible if dissipative effects (friction, viscosity, finite temperature differences, etc.) are present.

When the piston is loaded by infinitesimally small masses added one after another, the motion can be made arbitrarily slow and the system stays almost in equilibrium throughout. In this limiting case the forward and reverse paths coincide and the process is reversible. If, however, a finite mass is dropped suddenly on the piston, the piston will accelerate and oscillate; viscous dissipation and internal friction convert mechanical energy into heat and the oscillation dies out, leaving the system in a new equilibrium. That sudden process is irreversible.

Cause of irreversibility (common mechanisms)

• Friction and viscous dissipation: mechanical energy lost as heat during motion (e.g., piston friction, internal viscosity of fluids).
• Finite driving gradients: finite pressure, temperature or chemical potential differences that force the system through non-equilibrium states (for example, heat conduction across a finite ΔT).
• Unrestrained expansion: free expansion of a gas into vacuum produces entropy and is irreversible.
• Mixing of different substances: spontaneous mixing (even of ideal gases) is irreversible.
• Inelastic deformation and plastic work: material dissipation during irreversible deformation.
• Electrical resistance: Joule heating when current flows through a resistor.
• Chemical reactions with finite affinity: reactions proceeding with a finite difference in chemical potential are irreversible.

Precise criterion for reversibility

A process is thermodynamically reversible if, after reversing the direction of all driving forces, the system and surroundings can be returned to their exact initial states without any net changes in the rest of the universe. Equivalently, the process must produce zero entropy generation. This last statement leads naturally to the entropy criterion below.

Entropy and irreversibility

Define the total entropy differential of an isolated universe (system + surroundings) as dS_total. Then the second law gives the inequality

dS_total = dS_system + dS_surroundings ≥ 0

For a reversible process dS_total = 0. For an irreversible process dS_total > 0. Thus entropy generation is the quantitative measure of irreversibility.

Work and heat for reversible processes

Only for processes that proceed through equilibrium states can the instantaneous intensive variables (pressure, temperature) be assigned uniquely to the system and used to evaluate work and heat in the familiar integral form.

For a reversible mechanical process in a closed system the work exchanged is

W_rev = ∫ P_int dV

where P_int is the internal (equilibrium) pressure of the system at each instant. If the process is irreversible, internal pressure is not uniquely defined during transient non-equilibrium states and the simple integral above referring to system pressure is not valid. In many irreversible practical cases the work can be computed using the external pressure (for example, when expansion is opposed by a known constant external pressure),

W = ∫ P_ext dV

but this does not represent the maximum work extractable between the same end states; reversible work is an upper bound.

Heat transfer and reversibility

Heat transfer is reversible only in the limiting case of an infinitesimal temperature difference between system and surroundings. If heat flows across a finite temperature difference ΔT, the transfer is irreversible because entropy is generated. In the reversible limit the exchanged heat δQ_rev is related to entropy change as

δQ_rev = T dS

Examples of reversible and irreversible processes

• Reversible example: an idealised quasi-static compression or expansion performed by adding or removing infinitesimal weights so that the system stays in equilibrium; heat transfer across an infinitesimal temperature difference.
• Irreversible examples: rapid compression by sudden addition of finite mass causing oscillation and viscous dissipation; free expansion of a gas into vacuum; heat conduction across a finite temperature difference; spontaneous mixing of two gases; flow through a throttling valve with viscous losses.

Relation between quasi-static and reversible

Quasi-static means the system passes through a continuous sequence of equilibrium states. Reversible requires, additionally, absence of dissipative effects (friction, viscosity, finite ΔT, etc.). Thus:

• All reversible processes are quasi-static.
• Not all quasi-static processes are reversible if dissipation is present.

Practical consequences and engineering applications

Although strictly reversible processes are idealisations that cannot be realised in finite time with real substances, the concept is central to engineering because reversible processes set upper bounds on performance. For instance, the maximum work obtainable or the maximum thermal efficiency of a heat engine operating between two temperatures is achieved only by reversible (Carnot) processes; any irreversibility reduces efficiency. In civil engineering practice the ideas are relevant in the design and analysis of HVAC and refrigeration systems, power plants used for building services, thermal insulation and heat-flow problems in structures, and energy efficiency studies.

Recognising sources of irreversibility permits targeted improvements: reducing flow resistance to lower viscous losses, increasing heat exchange area or reducing ΔT to reduce entropy generation in heat transfer, and avoiding abrupt expansions or compressions where possible.

Summary and key points

• Reversible process: an idealised process that can be reversed with both system and surroundings restored to initial states; occurs only without dissipative effects and in the quasi-static limit; produces zero entropy generation.
• Irreversible process: real processes with dissipative effects and finite gradients; cannot be reversed to restore the universe exactly to its initial condition; produce positive entropy generation.
• Quasi-static: proceeds infinitely slowly through equilibrium states; necessary for reversibility but not sufficient.
• Work evaluation: reversible mechanical work can be obtained by integrating internal pressure, W_rev = ∫ P_int dV; for irreversible processes internal pressure is not uniquely defined during transients.
• Entropy criterion: dS_total = dS_system + dS_surroundings ≥ 0; equality holds only for reversible processes.