8.1 Irreversible Thermodynamics and Entropy Production

Irreversible thermodynamics explores processes that can't be undone without changing the system or surroundings. It's all about entropy production - the measure of disorder that always increases in isolated systems. This concept is crucial for understanding real-world energy transformations.

From heat transfer to chemical reactions, irreversible processes shape our world. By studying entropy production rates and dissipative forces, we can optimize industrial processes, analyze biological systems, and improve the efficiency of engines and refrigerators. It's thermodynamics in action!

Irreversible Processes and Entropy Production

Defining Irreversible Processes

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• Irreversible processes are thermodynamic processes that cannot be reversed without leaving a change in the system or its surroundings
  • They are characterized by an increase in entropy
• The second law of thermodynamics states that the total entropy of an isolated system always increases over time, and this increase is driven by irreversible processes
• Examples of irreversible processes include:
  • Heat transfer across a finite temperature difference
  • Fluid flow through a pipe with friction
  • Chemical reactions

Entropy Production in Irreversible Processes

• Entropy production is the generation of entropy due to irreversible processes within a system
  • It is always positive for irreversible processes and zero for reversible processes
• The entropy production rate is the rate at which entropy is generated within a system due to irreversible processes
  • It is expressed as the product of the flux and the conjugate force for each irreversible process

Entropy Production in Irreversible Processes

Expressions for Entropy Production

• The entropy production rate for heat transfer is given by:
  • $\sigma = J_q * (1/T_c - 1/T_h)$, where $J_q$ is the heat flux, $T_c$ is the cold reservoir temperature, and $T_h$ is the hot reservoir temperature
• For fluid flow through a pipe, the entropy production rate is:
  • $\sigma = J_v * (\Delta p/T)$, where $J_v$ is the volumetric flow rate, $\Delta p$ is the pressure drop, and $T$ is the absolute temperature
• In the case of chemical reactions, the entropy production rate is:
  • $\sigma = J_r * (A/T)$, where $J_r$ is the reaction rate, $A$ is the affinity of the reaction, and $T$ is the absolute temperature
  • The affinity $A$ is defined as the negative of the Gibbs free energy change of the reaction per mole of the reaction progress variable
• For diffusion processes, the entropy production rate is:
  • $\sigma = J_i * (\Delta \mu_i/T)$, where $J_i$ is the diffusive flux of species $i$, $\Delta \mu_i$ is the chemical potential gradient of species $i$, and $T$ is the absolute temperature

Total Entropy Production Rate

• The total entropy production rate in a system is the sum of the entropy production rates for all irreversible processes occurring within the system
  • This includes contributions from heat transfer, fluid flow, chemical reactions, and diffusion processes

Dissipative Forces in Irreversible Thermodynamics

Nature of Dissipative Forces

• Dissipative forces are non-conservative forces that oppose the motion or change in a system and lead to the dissipation of energy as heat
  • They are responsible for the irreversibility of processes
• Examples of dissipative forces include:
  • Friction
  • Viscosity
  • Electrical resistance
  • Chemical reaction barriers

Fluxes, Conjugate Forces, and Entropy Production

• Dissipative forces are associated with fluxes (e.g., heat flux, mass flux, or reaction rate) and their conjugate forces (e.g., temperature gradient, concentration gradient, or affinity)
• The product of a flux and its conjugate force represents the rate of entropy production due to the corresponding irreversible process
• The presence of dissipative forces leads to the production of entropy and the irreversible dissipation of energy, which limits the efficiency of real-world processes

Rayleigh Dissipation Function

• The Rayleigh dissipation function is a measure of the rate at which mechanical energy is dissipated into heat due to dissipative forces in a system
  • It quantifies the irreversible energy dissipation associated with dissipative forces

Irreversible Thermodynamics in Real-World Systems

Efficiency and Performance Analysis

• Irreversible thermodynamics can be applied to analyze the efficiency and performance of various real-world systems, such as:
  • Heat engines
  • Refrigerators
  • Fuel cells
• In heat engines, irreversible processes such as heat transfer across finite temperature differences and friction lead to entropy production and reduce the efficiency below the Carnot efficiency
• Refrigerators and heat pumps rely on the irreversible process of heat transfer from a cold reservoir to a hot reservoir, which requires work input and leads to entropy production

Industrial Process Optimization

• Irreversible thermodynamics can be used to optimize the design and operation of industrial processes, such as:
  • Chemical reactors
  • Distillation columns
  • Heat exchangers
• By minimizing entropy production, the efficiency and performance of these processes can be improved

Biological Systems

• In biological systems, irreversible processes such as metabolism, transport, and signaling are essential for maintaining life and are subject to the principles of irreversible thermodynamics
• The efficiency of energy conversion in biological processes is limited by entropy production, and living organisms must continuously dissipate energy to maintain their ordered state
• Examples of irreversible processes in biological systems include:
  • Cellular respiration
  • Photosynthesis
  • Ion transport across cell membranes