6.3 Entropy generation and irreversibility

Entropy generation quantifies irreversibility in thermodynamic processes. It's always non-negative, with zero for reversible processes and positive for irreversible ones. Understanding entropy generation helps assess process efficiency and identify areas for improvement.

Calculating entropy generation involves heat transfer rates, temperatures, and system entropy changes. Factors like heat transfer, friction, mixing, and chemical reactions contribute to entropy generation. Minimizing entropy generation reduces lost work and improves system efficiency in real-world applications.

Entropy Generation and Irreversibility

Entropy generation and irreversibility

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• Entropy generation quantifies entropy produced within a system during a process due to irreversibilities caused by friction, heat transfer through a finite temperature difference, mixing, and chemical reactions
• Second law of thermodynamics states entropy generation is always non-negative for any real process
  • Reversible processes have zero entropy generation
  • Irreversible processes always have positive entropy generation
• Entropy generation measures the irreversibility of a process greater entropy generation indicates a more irreversible process

Calculation of entropy generation

• Entropy generation for a process calculated using the equation: $\dot{S}_{gen} = \sum \frac{\dot{Q}}{T} - \frac{dS}{dt}$
  • $\dot{S}_{gen}$ represents the rate of entropy generation
  • $\dot{Q}$ represents the heat transfer rate
  • $T$ represents the absolute temperature at which the heat transfer occurs
  • $\frac{dS}{dt}$ represents the rate of change of entropy of the system
• For a closed system undergoing a process, entropy generation calculated as: $S_{gen} = \Delta S_{total} - \frac{Q}{T}$
  • $\Delta S_{total}$ represents the total change in entropy of the system and its surroundings
  • $Q$ represents the heat transfer between the system and its surroundings
  • $T$ represents the absolute temperature at which the heat transfer occurs
• In the case of an adiabatic process (no heat transfer), entropy generation equals the change in entropy of the system: $S_{gen} = \Delta S_{system}$

Factors in entropy generation

• Heat transfer through a finite temperature difference
  • Entropy generated when heat transferred between two reservoirs at different temperatures (hot reservoir and cold reservoir)
  • Entropy generation proportional to heat transfer and inversely proportional to temperature at which transfer occurs
• Friction in moving parts
  • Friction converts mechanical work into heat, increasing system entropy
  • Entropy generation due to friction proportional to work lost to friction and inversely proportional to absolute temperature
• Mixing of fluids
  • Entropy generated when two or more fluids mix due to irreversible nature of mixing process (oil and water)
  • Entropy generation depends on fluid properties and mixing process
• Chemical reactions
  • Chemical reactions can generate entropy due to irreversible nature of reaction (combustion)
  • Entropy generation depends on extent of reaction and temperature at which it occurs

Lost work from irreversibility

• Lost work represents the difference between maximum theoretical work obtainable from a process and actual work obtained
  • Maximum theoretical work obtainable if process were reversible
  • Actual work always less than maximum theoretical work due to irreversibilities
• Lost work directly related to entropy generation of the process: $W_{lost} = T_0 \cdot S_{gen}$
  • $T_0$ represents the absolute temperature of the surroundings
  • $S_{gen}$ represents the entropy generation of the process
• Presence of lost work reduces system efficiency
  • Greater lost work leads to lower system efficiency (heat engines)
  • Minimizing entropy generation helps reduce lost work and improve system efficiency
• In real-world systems, important to identify and minimize sources of irreversibility to maximize efficiency and minimize lost work (power plants, refrigerators)