4.1 Reversible and Irreversible Processes

Reversible and irreversible processes are key concepts in thermodynamics. They help us understand how energy changes and flows in real-world systems. Reversible processes are ideal, while irreversible ones reflect reality.

The second law of thermodynamics ties these ideas to entropy, which always increases in isolated systems. This law explains why some processes happen spontaneously and others don't, shaping our understanding of energy efficiency and natural phenomena.

Reversible and Irreversible Processes

Reversible vs irreversible processes

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• Reversible processes occur infinitely slowly, allowing the system to remain in equilibrium with its surroundings at all times
  • Can be reversed without any net change in the system or surroundings
  • Require infinitesimal changes in thermodynamic variables (pressure, volume, temperature)
  • Idealized processes that do not occur in reality but serve as a theoretical limit (frictionless motion, perfect insulation)
• Irreversible processes occur at a finite rate, causing the system to deviate from equilibrium with its surroundings
  • Cannot be reversed without net changes in the system or surroundings
  • Involve finite changes in thermodynamic variables
  • Real-world processes that always result in an increase in entropy (heat transfer, gas expansion, mixing)
  • An adiabatic process, where no heat is exchanged with the surroundings, is typically irreversible in practice

Second law and irreversibility

• The second law of thermodynamics states that the total entropy of an isolated system always increases over time
  • Entropy measures the disorder or randomness of a system (gas molecules, energy distribution)
• Irreversible processes always lead to an increase in the total entropy of the universe
  • Heat transfer from a hot object to a cold object, gas expansion into a vacuum, and mixing of two gases increase entropy
• Heat naturally flows from a higher temperature to a lower temperature
  • This process is irreversible, as heat cannot spontaneously flow from a colder object to a hotter object without external work being done
• The second law places constraints on the direction of heat flow and the efficiency of heat engines
  • No heat engine can be 100% efficient, as some heat must always be rejected to a low-temperature reservoir (exhaust, cooling towers)
  • The Carnot cycle represents the most efficient theoretical heat engine operating between two temperature reservoirs

Entropy and process spontaneity

• The change in entropy $(\Delta S)$ determines the spontaneity of a process
  1. For a spontaneous process, $\Delta S_\text{universe} > 0$ (ice melting, gas expanding)
  2. For a non-spontaneous process, $\Delta S_\text{universe} < 0$ (water freezing, gas compressing)
  3. For a process at equilibrium, $\Delta S_\text{universe} = 0$ (sealed container, isolated system)
• The entropy change of the universe is the sum of the entropy changes of the system and its surroundings
  • $\Delta S_\text{universe} = \Delta S_\text{system} + \Delta S_\text{surroundings}$
• The entropy change of a system can be calculated using the following equations:
  • For a reversible process: $\Delta S = \int \frac{dQ_\text{rev}}{T}$, where $dQ_\text{rev}$ is the heat exchanged reversibly and $T$ is the absolute temperature
  • For an irreversible process: $\Delta S > \int \frac{dQ}{T}$, where $dQ$ is the actual heat exchanged
  • The Clausius inequality states that for any cyclic process, $\oint \frac{dQ}{T} \leq 0$, with equality holding only for reversible processes
• The entropy change of the surroundings can be calculated using: $\Delta S_\text{surroundings} = -\frac{Q}{T_\text{surroundings}}$, where $Q$ is the heat exchanged with the surroundings and $T_\text{surroundings}$ is the absolute temperature of the surroundings

Thermodynamic potentials and efficiency

• Free energy is a thermodynamic potential that combines the internal energy, temperature, and entropy of a system
  • It helps determine the spontaneity and maximum work output of processes at constant temperature and pressure
• Thermodynamic efficiency measures the ratio of useful work output to total energy input in a thermodynamic process or cycle
  • It is always less than 100% due to irreversibilities and heat losses