Chemical Engineering \ Thermodynamics \ Non-Equilibrium Thermodynamics

Non-equilibrium thermodynamics is a vital sub-discipline within chemical engineering that investigates the behavior of thermodynamic systems not in equilibrium. While classical thermodynamics primarily focuses on systems in a static or equilibrium state, non-equilibrium thermodynamics deals with dynamic systems where processes such as chemical reactions, heat transfer, and mass transfer occur continuously.

Key Concepts

1. Irreversible Processes:
   Non-equilibrium thermodynamics primarily concerns itself with irreversible processes. Unlike reversible processes, which can be undone without any lasting change to the system or the environment, irreversible processes result in the production of entropy and the dissipation of energy.

2. Entropy Production:
   In non-equilibrium systems, entropy production is a central concept. According to the second law of thermodynamics, entropy in an isolated system never decreases. For non-equilibrium processes, entropy production (\( \sigma \)) can be quantified as:
   \[
   \sigma = \sum \left( \frac{J_i}{T} \right) \cdot X_i
   \]
   where \( J_i \) are fluxes such as heat flux or particle flux, \( T \) is the temperature, and \( X_i \) are the corresponding thermodynamic forces like temperature gradient or concentration gradient.

3. Transport Phenomena:
   Non-equilibrium thermodynamics heavily overlaps with the study of transport phenomena, which involves the movement of mass, energy, and momentum in a system. The primary equations governing these phenomena include:

   • Fourier’s Law for heat conduction: \( \mathbf{q} = -k \nabla T \)
   • Fick’s Law for diffusion: \( \mathbf{J} = -D \nabla c \)
   • Newton’s Law of Viscosity for momentum transfer: \( \tau = -\mu \frac{\partial u}{\partial y} \)

4. Linear and Non-linear Regimes:
   Non-equilibrium thermodynamics differentiates between linear and non-linear regimes. In the linear regime, the fluxes and forces are related by linear relationships, which is often the case near equilibrium. Far from equilibrium, systems exhibit non-linear behavior, requiring more complex models to describe the interactions.

5. Onsager’s Reciprocal Relations:
   In the linear regime of non-equilibrium thermodynamics, Lars Onsager developed reciprocal relations to describe the proportionality between thermodynamic fluxes and forces:
   \[
   J_i = \sum_j L_{ij} X_j
   \]
   where \( L_{ij} \) are the Onsager coefficients, which are symmetric (\( L_{ij} = L_{ji} \)) under certain conditions, indicating coupled processes like thermal diffusion and Soret effect.

Applications

Non-equilibrium thermodynamics has profound applications in chemical engineering, including:

• Reaction Engineering: Understanding the rates of chemical reactions away from equilibrium and optimizing reaction conditions to maximize yield and efficiency.
• Biochemical Engineering: Analyzing transport in biological systems, where non-equilibrium processes are fundamental to cellular function and metabolic activities.
• Energy Systems: Efficient design and analysis of energy systems, including fuel cells, batteries, and thermal energy storage systems, where non-equilibrium processes dictate performance.
• Environmental Engineering: Modeling pollutant dispersion, chemical spills, and waste treatment processes, all of which involve non-equilibrium mass transfer and chemical reactions.

By studying non-equilibrium thermodynamics, chemical engineers gain critical insights into the behavior of dynamic systems, enabling the design of more efficient and sustainable industrial processes.