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THERMODYNAMICS & CHEMICAL PROCESS
DESIGN AND ANALYSIS
Below is a brief introduction of the Thermodynamics Modeling required to study real-world physics and chemistry problems.
I have used Thermodynamics to both design and analyze the following systems
- Calculated the effect of ionic concentrations on the yields for electrolytic systems (PEFC fuel cells and electrolyzer for chlor-alkali system)
- Performed Mass and Energy calculations for chemical process production trains.
- Designed Heaters required for manufacturing processes
- Calculated characteristics (Maximum Specific Energy, Overpressure, etc.) of Explosive Reaction Processes.
- Calculated diffusion of organic molecules in polycarbonates and polyolefins.
- Use Fault Tree and Event Tree Analysis to perform failure analysis for Chemical Reaction Processes.
The field of Thermodynamics is one of the few self-contained areas of study in the physical sciences that is developed on the basis of only a moderate knowledge of mathematics (partial differential and integral equations). It can be formally defined as the mathematical treatment of the relation of heat to mechanical, chemical and other forms of energy. Classical thermodynamics is rooted in the three basic laws that are summarized below.
- Zeroth Law - If two systems are in thermal equilibrium with a third system then they are in thermal equilibrium with each other.
- First Law - The work done on a body in an adiabatic process, not involving changes of the body's kinetic or potential energy, is equal to the increase in the state variable of Internal Energy. This is the thermodynamic statement for the fundamental principle of the Conservation of Energy.
- Second Law - The possibility or impossibility of the process A to B and B to A depends entirely on the nature of the states A and B at the beginning and end of the process. We may therefore expect to find a state function of these variables whose special characteristic is to show whether or not the process will go from A to B or from B to A. We will call this state function the Entropy S, which is defined for a reversible process as dS ≡ dq/T. The change of Entropy in a closed system (where energy can be exchanged but not matter) that is adiabatically isolated can never decrease; it increases in an irreversible process and is equal to zero in a reversible process. The Second Law of Thermodynamics gives rise to the following observed rules:
- Heat can never pass spontaneously from a body at a lower temperature to a body at a higher temperature.
- The Entropy of a system is a measure of its randomness, or disorder.
- Since all natural changes in the universe are irreversible, the entropy of universe increases in the course of every natural change.
There is also a Third Law that is a "statistical" addition to the first three so-called "classical" Laws of Thermodynamics. And it is of more interest to chemists than physicists because it has been historically used to calculate equilibrium constants of chemical reactions from the thermal properties of reactants.
- Third Law - The change in Entropy of a substance approaches zero as its temperature approaches absolute zero (0o K). For the purposes of this web page, this Third Law will not be mentioned further.
A series of four differential equations have been developed that mathematically contain the totality of the fundamental theory contained in the first three laws of thermodynamics.
- dE ≡ dq + dw
where dE is the Internal Energy of a system, dq is the heat absorbed by the system, and dw is the work done on the system as the system changes between two states.
- dS ≡ dq/T = 0
is valid for a reversible process where dS is the change in Entropy as the system changes between two states.
- dS ≡ dq/T ≥ 0
is valid for an irreversible process where dS is the change in Entropy as the system changes between two states.
- dE = TdS − PdV + Σμidni
for each of the "i" homogeneous parts of a system as the system changes between two states. P is the (constant) pressure of the system, and dV is the volume change of the system,
These four equations, along with the following "convenient" state functions listed below allow many important quantities to be calculated. Some commonly used aspects of these four convenience functions are briefly defined below but it must be remembered that as state functions there are many definitions that can be derived though partial (and exact) differential equations.
- Enthalpy is defined as H ≡ E + PV. The specialized Enthalpy of Formation is the change in Energy that occurs when a compound is formed from its elements in their "standard" state. A positive Enthalpy of Formation indicates that energy must be provided in order for the reaction to proceed (the reaction is said to be endothermic). A negative Enthalpy of Formation indicates that energy is evolved as the reaction spontaneously occurs (the reaction is said to be exothermic).
- Gibbs Free Energy is defined as G ≡ H − TS. The quantity ΔG = ΔH − TΔS represents the driving force of a reversible chemical change. When ΔG is negative the reaction will be spontaneous in the direction as written; when ΔG is positive the reverse of "the reaction as written" will be spontaneous. The magnitude of the ΔG is a measure of the extent to which the reaction will go to completion.
- Helmholtz Free Energy is defined as A ≡ E − TS - The quantity ΔA is a measure of the maximum attainable work in a process in which 1) the only heat transferred to the system is from a heat reservoir and the initial and final temperatures of the system are both equal to the temperature of the heat reservoir, which remains constant throughout the process.
- Chemical Potential is defined through exact differential as μi ≡ (∂G/∂ni)T,P,nj ≡ (∂U/∂ni)S,V,nj ≡ (∂H/∂ni)S,P,nj ≡ (∂A/∂ni)T,V,nj - Recall that a temperature difference determines the tendency of heat to pass from one body to another and the pressure difference determines the tendency of bodily movement. In a similar fashion, the difference in chemical potential may be regarded as either the cause of a chemical reaction or the tendency of a substance to diffuse from one phase into another.
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