The anthracite smokers of eastern pennsylvania: PS2 (g)P_{S_2 (g)} -T stability diagram by TL analysis

Coal seams and culm banks associated with mine fires in the anthracite region of eastern Pennsylvania have been burning for decades. Many of the fires may have ignited by spontaneous combustion or by the burning of trash. Minerals associated with the combustion of anthracite form by the condensation of gas exhaled through surficial gas vents or anthracite smokers. A Pressure-Temperature (P-T) stability diagram is constructed for the condensation of orthorhombic sulfur from anthracite gas using Thermodynamic Loop Analysis (TL analysis). This method of analyzing chemical systems incorporates Kirchhoff's Law into a four step procedure structured around a closed thermodynamic cycle or thermodynamic loop. The four steps, referred to us The Four S S of Thermodynamic Loop Analysis, include: (1) Set Up—graphical characterization of the problem. (2) Sum—the application of thermodynamic principles. (3) Substitute—the use of materials data available from the literature, and (4) Solve—computation of one or more variables. The example presented demonstrates that thermodynamic loops can incorporate any number of polymorphic phase transformations. In addition, thermodynamic loop analysis is applicable to any geologic process involving the condensation of minerals from a gas. The stability diagram derived by TL analysis may have applicability in monitoring the release of sulfur gas into the atmosphere.     

The Internal Energy of a PV = RT Gas: A Univariable or Multivariable Function

Historically, the characterization of the internal energy of a simple gas is based on free expansion experiments and imprecise use of the word function, which is rigorously defined in mathematics. Univariable equations of state show that the internal energy of simple monatomic, diatomic, and polyatomic gases can be expressed as a function of temperature only. However, multivariable equations of state derived from composite functions confirm that the internal energy of these gases can in each situation also be expressed as a function of pressure and volume only. It is essential that the mathematical definition of the word function be adhered to in science because it is fundamental for the formulation of the calculus, a mathematical tool essential for solving a variety of thermodynamics problems.     

The anthracite smokers of eastern pennsylvania:P_{S_2 (g)} -T stability diagram by TL analysis

Coal seams and culm banks associated with mine fires in the anthracite region of eastern Pennsylvania have been burning for decades. Many of the fires may have ignited by spontaneous combustion or by the burning of trash. Minerals associated with the combustion of anthracite form by the condensation of gas exhaled through surficial gas vents or “anthracite smokers.” A Pressure-Temperature (P-T) stability diagram is constructed for the condensation of orthorhombic sulfur from anthracite gas using “Thermodynamic Loop Analysis” (TL analysis). This method of analyzing chemical systems incorporates Kirchhoff's Law into a four step procedure structured around a closed thermodynamic cycle or “thermodynamic loop.” The four steps, referred to us “The Four S ′S of Thermodynamic Loop Analysis,” include: (1) “Set Up”—graphical characterization of the problem. (2) “Sum”—the application of thermodynamic principles. (3) “Substitute”—the use of materials data available from the literature, and (4) “Solve”—computation of one or more variables. The example presented demonstrates that thermodynamic loops can incorporate any number of polymorphic phase transformations. In addition, thermodynamic loop analysis is applicable to any geologic process involving the condensation of minerals from a gas. The stability diagram derived by TL analysis may have applicability in monitoring the release of sulfur gas into the atmosphere.     

Preface

Mathematical Geosciences -