2.1 Fundamentals of thermodynamics in separations

Thermodynamics is key to understanding separation processes. The laws of thermodynamics govern energy conservation, entropy generation, and efficiency limits in separations like distillation and extraction. Energy balances are crucial for both closed and open systems.

Important concepts include enthalpy, entropy, and Gibbs free energy. These help determine process spontaneity, equilibrium conditions, and driving forces in separations. Thermodynamic efficiency compares ideal to real separations, calculating the minimum work required for processes like gas separation.

Thermodynamic Principles in Separation Processes

Thermodynamics in separation processes

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• First Law of Thermodynamics governs energy conservation in separations, quantifies internal energy changes, work done, and heat transfer
• Second Law of Thermodynamics addresses entropy generation, distinguishes reversible from irreversible processes, and sets efficiency limits (distillation, extraction)
• Energy balances crucial for closed systems (batch distillation) and open systems with mass flow (continuous distillation column)

Thermodynamic concepts for separations

• Enthalpy measures heat content, relates to internal energy and PV work, critical in phase transitions (vaporization in distillation)
• Entropy quantifies system disorder, changes during mixing and separation, Third Law establishes absolute entropy scale
• Gibbs free energy combines enthalpy and entropy effects, determines process spontaneity at constant T and P, links to chemical potential in separations (membrane processes)

Thermodynamic Analysis and Calculations

Feasibility of separation processes

• Spontaneity determined by Gibbs free energy change ($\Delta G$), relates to enthalpy and entropy changes
• Equilibrium conditions crucial in chemical (reactive distillation) and phase equilibrium (vapor-liquid equilibrium in distillation)
• Driving forces include concentration gradients (osmosis), temperature gradients (thermal diffusion), pressure differences (reverse osmosis)
• Thermodynamic efficiency compares ideal to real separations, calculates minimum work required (gas separation)

Calculation of thermodynamic properties

• Equations of state model fluid behavior: Ideal gas law for low pressure, Van der Waals for real gases, Peng-Robinson for complex mixtures
• Thermodynamic tables provide property data: Steam tables for water/steam systems, refrigerant tables for cooling cycles, psychrometric charts for air-water mixtures
• Property estimation methods include corresponding states principle and generalized correlations for unknown substances
• Fugacity and activity coefficients quantify non-ideal behavior in gas and liquid mixtures respectively
• Partial molar properties describe component contributions in mixtures (partial molar volume in liquid solutions)
• Excess properties characterize non-ideal mixing behavior (excess Gibbs energy in azeotropic mixtures)