The Volume 5 Sequel and Thermodynamics
A Volume 5 sequel to Volumes 1 – 4 of Elsevier’s Coal and Peat Fires: A Global Perspective will include a chapter that presents a technique using a variant of Kirchhoff’s law to derive equations that express pressure (P) as a function of temperature (T). When any of these equations are graphed, the result is a P-T stability diagram for a phase nucleated from coal-fire gas as well as other gases, including volcanic.
Coal-Fire Gas Vents
Coal-fire gas vents are openings through which the by-products of coal combustion are transported. These vents are circular to semi-circular in shape but may include linear or curved fissures that are usually non-polygonal, as in the case of joints and faults (Stracher, 2007, p. 91 – 96).
The by-products of coal combustion include gas and possibly solid and liquid particulates such as ash and water, respectively. Any such exhalation from a vent is referred to as smoke, especially when visible. Coal-fire gas analyses typically include 40 – 50 compounds, many of which are toxic (Stracher, 2010).
Nucleation of Solids
Solids such as minerals that encrust gas vents and fissures can form by a number of isochemical or mass-transfer processes. These are discussed in Stracher (2007, p. 91 – 96). The thermodynamic loop (TL) for Se and the sulfur P-T stability diagram in this article are representative of the isochemical process of sublimation, but another isochemical process is gas-liquid-solidification (GLS). The more complicated processes of mass transfer include gas reaction ±liquid-solidification (GRLS), gas-altered substrate (GAS), gas-liquid-precipitation (GLP), and gas-liquid-altered substrate (GLAS).
Thermodynamic Loop
A thermodynamic loop is a graphical-based analytical tool useful for solving simple to complex chemical-thermodynamics problems. The analysis of a TL is based on a variant of Kirchhoff’s law used to analyze electrical circuits. These loops are applicable to any changes in a thermodynamic “state function” including enthalpy (H), entropy (S), and Gibbs free energy (G). State functions are “path independent” and as discussed in introductory physics, include the work done by gravitational and electrical forces. A thermodynamic loop is defined by the property:
where Δθ designates the change in a thermodynamic state function between the tail and arrow head or the arrow head and tail in a thermodynamic loop. An example of a TL for the nucleation of solid Se (selenium) from Se gas is illustrated at the beginning of this article.
A TL is graphically constructed by writing a sequence of chemical reactions and by connecting the phases in and between the reactions with arrows. For example, in the Se TL above, the standard state reaction is written (State 3). Depending on the thermodynamic data bank used, the standard state pressure of an ideal gas, for example, that is insoluble in a condensed phase with which it is in contact is 1 atm or 1 bar pressure at any temperature. After the standard state reaction is written, the reaction in question is written (State 1 in the Se TL). Then, inbetween these two reactions are written any known phase-transformations and the temperatures at which they occur. In the Se TL, the only such reaction is Se(s) –> Se(l) at 494 K.
Summing around the loop in either a counterclockwise or clockwise direction; using the equations ΣΔH=0 and ΣΔS=0 where ΔH and ΔS are state-function changes, it is possible to calculate the enthalpy and entropy changes for temperature-dependent transformations in a TL by integrating heat capacities as a function of temperature. This would include, for example, between 494 K and 957 K on the right side of the Se TL above. Then, once ΔHTr/T and ΔSTr/T are calculated for State 1 in the Se TL, the Gibbs free energy criteria for equilibrium in that state, namely, ΔGTr/T =ΔHTr/T-TΔSTr/T=0 is used to derive an equation that when graphed, represents the equilibrium graph of pressure versus temperature for the phase transformation in question; in this case it would be for Se(g)–> Se(s).
This entire mathematical process is presented in Stracher (1995) for the nucleation of orthorhombic sulfur from sulfur gas. Analogous calculations will be done for Se and other phases in Volume 5. The P-T stability diagram for the nucleation of S, calculated by Stracher (1995); illustrated in Stracher (2010, p. 135-153); with color modifications in this SciTech Connect article is illustrated below; followed by an illustration of sulfur nucleated on a waste pile in a South African coal mine. On the curve between orthorhombic sulfur and sulfur gas, ΔG = 0; these two phases co-exist in equilibrium. When ΔG < 0 the transformation of sulfur gas to orthorhombic sulfur is spontaneous.
P-T stability diagrams have environmental implications because they indicate the pressures and temperatures at which gas from a coal fire or other combustion process may be exhaled into the atmosphere or nucleated into a solid phase, suggesting possible atmospheric or terrestrial pollution.
About the Authors
Dr. Glenn B. Stracher obtained his Ph.D. in Geology from the University of Nebraska-Lincoln where he also studied Engineering Mechanics. During his graduate studies, he studied the structural geology and the metamorphic petrology of the Whitehall mylonite zone in the SE Adirondack Mountain Highlands of New York State. He is the senior editor of Elsevier’s four-volume book Coal and Peat Fires: A Global Perspective and is editing Volume 5 of this book series. Dr. Stracher is Professor Emeritus at East Georgia State College in Swainsboro, Georgia. His web page is: http://faculty.ega.edu/facweb/stracher/stracher.html
Dr. Yelena V. White obtained her Ph.D. in Physics from Vanderbilt University in Nashville, Tennessee. During her graduate studies, she worked on laser-induced effects on surfaces and interfaces. She concentrated on laser spectroscopy and laser micromachining for microfluidic devices during her post-doctoral research and has expertise in scanning electron microscopy. Dr. White teaches calculus-based physics at East Georgia State College in Swainsboro, Georgia.
Dr. Jun Li obtained his Ph.D. in Engineering (thermodynamics) from the National University of Singapore. His main research interests include underground coal fires, deep geothermal energy utilization, and micro-scale combustion. His underground coal-fires research focuses on coupled heat and mass transport that plays a key role in determining the propagation of fire-reaction zones. Dr. Li teaches combustion engineering at Tianjin University, China.
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