Chemical Engineering \ Thermodynamics \ Equilibrium Thermodynamics

Description:

Equilibrium Thermodynamics is a fundamental sub-discipline within the field of Chemical Engineering that focuses on the principles governing energy and matter transformations under conditions of thermodynamic equilibrium. In thermodynamics, equilibrium refers to a state wherein a system’s macroscopic properties such as pressure, temperature, and composition remain constant over time because the system has balanced all internal processes.

Key Concepts:

1. Thermodynamic Systems and Surroundings:

A thermodynamic system is defined as the specific portion of the universe under study, separated by boundaries from the surroundings, where exchanges of energy and matter may occur. Systems can be classified as isolated (no exchange of energy or matter), closed (exchange of energy but not matter), or open (exchange of both energy and matter).

2. State Functions:

State functions are properties that depend only on the current state of the system and not on the path by which the system arrived at that state. Key state functions in equilibrium thermodynamics include:

• Internal Energy (U): The total energy contained within a system.
• Enthalpy (H): Represents the total heat content of a system, defined as \( H = U + PV \), where \( P \) is pressure and \( V \) is volume.
• Entropy (S): A measure of the system’s disorder or randomness.
• Gibbs Free Energy (G): A state function used to predict spontaneity of processes at constant pressure and temperature, given by \( G = H - TS \), where \( T \) is temperature.

3. Laws of Thermodynamics:

Equilibrium thermodynamics is governed by the Four Laws of Thermodynamics:

• Zeroth Law: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This forms the basis for temperature measurement.
• First Law: The principle of conservation of energy. For a closed system, this is expressed as: \[ \Delta U = Q - W \] where \( \Delta U \) is the change in internal energy, \( Q \) is the heat added to the system, and \( W \) is the work done by the system.
• Second Law: Entropy of an isolated system always increases for an irreversible process, and remains constant for a reversible process. This is quantitatively expressed as: \[ \Delta S \geq \int \frac{dQ}{T} \]
• Third Law: As temperature approaches absolute zero, the entropy of a perfect crystal approaches a constant minimum.

4. Phase Equilibrium:

The study of phase equilibrium involves understanding how different phases coexist at equilibrium. For example, in a binary mixture, the equilibrium between liquid and vapor phases can be described by Raoult’s Law for ideal mixtures and more complex equations for non-ideal mixtures.

5. Chemical Equilibrium:

Chemical equilibrium occurs when the rate of a forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products. The equilibrium constant \( K \) is used to describe the ratio of product concentrations to reactant concentrations at equilibrium, and it can be expressed as:
\[
K = \frac{[C]^c[D]d}{[A]^a[B]b}
\]
for a general reaction \( aA + bB \rightleftharpoons cC + dD \).

Application:

In Chemical Engineering, equilibrium thermodynamics is critical for designing and optimizing chemical processes, such as reactors, separation units, and energy conversion systems. Engineers use these principles to determine conditions under which reactions yield desired products efficiently, to predict material behavior, and to enhance energy and resource utilization.

Understanding equilibrium thermodynamics not only supports the practical aspects of designing industrial processes but also provides insights into the fundamental behaviors of matter and energy, highlighting the intrinsic connections between different branches of science and engineering.