Rigorous Development of the Fixed Dead State Version of the Exergy Equation Suitable for Undergraduate Class Presentation and Coursework

Sheldon Jeter

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Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: Mechanical Engineering: Thermodynamics
Page Count: 11
DOI: 10.18260/1-2--41325
Permanent URL: https://peer.asee.org/41325
Download Count: 188

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Sheldon Jeter Georgia Institute of Technology

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Sheldon M. Jeter has mechanical engineering degrees from Clemson, the University of Florida, and Georgia Tech. He has been on the academic faculty at Georgia Tech since 1979 and will retire in August 2022. He has written over 250 refereed journal articles and conference papers and numerous research reports and other articles. He has supervised 16 Ph. D. graduates and numerous other research students. His research interests are thermodynamics, experimental engineering, heat and mass transfer, solar energy, and energy systems including concentrating solar power and other solar issues, building energy systems, and HVAC issues in health care facilities.

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Abstract

One general version and two special case of the control volume (CV) exergy equation are useful and even important in mechanical engineering education and practice. The versions are closely related and differ primarily with respect to the applicable “Dead State”, in which the matter in the thermodynamic system under consideration can perform no further useful work and therefore has zero exergy. In all dead states the matter in the system has come to ambient pressure and temperature. For the Restricted Dead State (RDS) the system is kept separate from its surrounding; in contrast, for the ultimate or General Dead State (GDS), the material in the system is allowed to blend and react with and become identical to the surroundings. A further constraint is to dictate that the material in a closed system maintains a fixed composition. This implies a Fixed (Composition) Dead State and a corresponding equation. For most simpler mechanical engineering applications, the FDS is the pertinent dead state. In the RDS case, the dead state is taken to exist when the material in the engineering system is at ambient temperature and pressure and, if capable of chemical or other change in composition, in internal chemical equilibrium as well. A common and important, but not always specifically identified, special case of the RDS is the FDS. This FDS is the state in which the composition of the material has not changed from its composition in the prevailing state within the system. Importantly, this FDS case applicable to the usual working fluids in closed heat engine, heat pump, refrigeration, fluid power, and similar systems. Such engineering systems are overall closed or control mass (CM) systems with components such as compressors, fans, and pumps or turbines, fluid motors, and power cylinders that are individual CV subsystems. Take note, that the control mass (CM) system is, of course, a trivial but important special case of the control volume. These two related forms of the Exergy Equation apply for situations when the matter in the overall CM system is always kept separate from the surrounding inert ambient atmosphere, which is typically called the “medium”: (1) Fixed Dead State Exergy Equation (FEE) cases in which the composition of the engineering system is constant and uniform throughout the system so that the FDS case applies and (2) Restricted Dead Sate Exergy Equation (REE) cases such as electrochemical or thermochemical exergy storage systems with chemical or other composition changes within the overall system under consideration. The alternative case applies when the engineering system is open to the surrounding inert medium. The medium in its minimal form can be just the surrounding gaseous atmosphere. This gaseous atmosphere can conceivably be as simple as a hypothetical single component “dry air”, but more likely the simplest worthwhile medium is “moist air” (water vapor and dry air) in HAVC and similar applications or a slightly more complicated mixture of dry gases (nitrogen, oxygen, argon, carbon dioxide) and water vapor. For desalination systems the medium must include the liquid saline ocean in equilibrium with the gaseous atmosphere. If more complex chemical processing applications are considered, an inert version of the solid crust of the earth must be included in the medium containing the most stable chemical versions of the ores or other inert feedstocks of interest. This case of the unrestricted version, which for convenience can be called the Generalized Exergy Equation, is not addressed herein but a streamlined and related presentation will be made available in a planned complementary publication and is available now in draft form on request from this author. Junior or senior students in mechanical or related engineering interested in thermal systems should be aware of the Exergy Equation at least. Such students should have finished the usual first or only semester thermodynamics course and be well aware of energy and entropy analysis and mass conservation, as well as some minimal physical chemistry. The required chemistry is mostly just stoichiometry, but some knowledge of chemical equilibrium and an appreciation of the chemical potential is necessary for application and appreciation of the FEE when composition changes are considered. Otherwise, the REE can be limited only to working or process fluids of fixed composition, for which the FDS is the applicable dead state. This FDS version appears to be the only version addressed in typical undergraduate textbooks, and it is probably the only version actually needed by typical students in mechanical and related disciplines. Given the basic preparation needed to understand and appreciate the REE, at least two approaches to its derivation are feasible (1) the typical textbook presentation which requires some heuristic justification of the dead state terms in the REE or (2) a purely rigorous derivation presented in the current paper, which actually requires barely more classroom time. The heuristic or shorthand derivation involves combining the time derivative CV energy and entropy equations and rather arbitrarily introducing the dead state extensive properties into the time derivative term. The alternative rigorous development relies instead on the always arbitrary definitions available for the reference properties for the entropy and enthalpy and recognizing the coupling of the internal energy and enthalpy. In this approach the expected dead state properties arise naturally, and the expected system and flow exergy terms also arise naturally. The result is an enhanced teaching and learning strategy that exemplifies a rigorous approach and emphasizes the scope and rigor of thermodynamics. The proposed paper will support a rigorous derivation and presentation of the FEE. The result supports a brief presentation that can be conducted in class without an excessive investment in time or be readily packaged into a video presentation for student-paced self-study. Ultimately, this presentation should be a useful addition to an elementary or intermediate thermodynamics course or any thermal and energy systems engineering course.

Citation
Format

Jeter, S. (2022, August), Rigorous Development of the Fixed Dead State Version of the Exergy Equation Suitable for Undergraduate Class Presentation and Coursework Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--41325

TY - CPAPER
AB - One general version and two special case of the control volume (CV) exergy equation are useful and even important in mechanical engineering education and practice. The versions are closely related and differ primarily with respect to the applicable “Dead State”, in which the matter in the thermodynamic system under consideration can perform no further useful work and therefore has zero exergy. In all dead states the matter in the system has come to ambient pressure and temperature. For the Restricted Dead State (RDS) the system is kept separate from its surrounding; in contrast, for the ultimate or General Dead State (GDS), the material in the system is allowed to blend and react with and become identical to the surroundings. A further constraint is to dictate that the material in a closed system maintains a fixed composition. This implies a Fixed (Composition) Dead State and a corresponding equation. For most simpler mechanical engineering applications, the FDS is the pertinent dead state. In the RDS case, the dead state is taken to exist when the material in the engineering system is at ambient temperature and pressure and, if capable of chemical or other change in composition, in internal chemical equilibrium as well. A common and important, but not always specifically identified, special case of the RDS is the FDS. This FDS is the state in which the composition of the material has not changed from its composition in the prevailing state within the system. Importantly, this FDS case applicable to the usual working fluids in closed heat engine, heat pump, refrigeration, fluid power, and similar systems. Such engineering systems are overall closed or control mass (CM) systems with components such as compressors, fans, and pumps or turbines, fluid motors, and power cylinders that are individual CV subsystems. Take note, that the control mass (CM) system is, of course, a trivial but important special case of the control volume. These two related forms of the Exergy Equation apply for situations when the matter in the overall CM system is always kept separate from the surrounding inert ambient atmosphere, which is typically called the “medium”: (1) Fixed Dead State Exergy Equation (FEE) cases in which the composition of the engineering system is constant and uniform throughout the system so that the FDS case applies and (2) Restricted Dead Sate Exergy Equation (REE) cases such as electrochemical or thermochemical exergy storage systems with chemical or other composition changes within the overall system under consideration.
The alternative case applies when the engineering system is open to the surrounding inert medium. The medium in its minimal form can be just the surrounding gaseous atmosphere. This gaseous atmosphere can conceivably be as simple as a hypothetical single component “dry air”, but more likely the simplest worthwhile medium is “moist air” (water vapor and dry air) in HAVC and similar applications or a slightly more complicated mixture of dry gases (nitrogen, oxygen, argon, carbon dioxide) and water vapor. For desalination systems the medium must include the liquid saline ocean in equilibrium with the gaseous atmosphere. If more complex chemical processing applications are considered, an inert version of the solid crust of the earth must be included in the medium containing the most stable chemical versions of the ores or other inert feedstocks of interest. This case of the unrestricted version, which for convenience can be called the Generalized Exergy Equation, is not addressed herein but a streamlined and related presentation will be made available in a planned complementary publication and is available now in draft form on request from this author.
Junior or senior students in mechanical or related engineering interested in thermal systems should be aware of the Exergy Equation at least. Such students should have finished the usual first or only semester thermodynamics course and be well aware of energy and entropy analysis and mass conservation, as well as some minimal physical chemistry. The required chemistry is mostly just stoichiometry, but some knowledge of chemical equilibrium and an appreciation of the chemical potential is necessary for application and appreciation of the FEE when composition changes are considered. Otherwise, the REE can be limited only to working or process fluids of fixed composition, for which the FDS is the applicable dead state. This FDS version appears to be the only version addressed in typical undergraduate textbooks, and it is probably the only version actually needed by typical students in mechanical and related disciplines.
Given the basic preparation needed to understand and appreciate the REE, at least two approaches to its derivation are feasible (1) the typical textbook presentation which requires some heuristic justification of the dead state terms in the REE or (2) a purely rigorous derivation presented in the current paper, which actually requires barely more classroom time. The heuristic or shorthand derivation involves combining the time derivative CV energy and entropy equations and rather arbitrarily introducing the dead state extensive properties into the time derivative term. The alternative rigorous development relies instead on the always arbitrary definitions available for the reference properties for the entropy and enthalpy and recognizing the coupling of the internal energy and enthalpy. In this approach the expected dead state properties arise naturally, and the expected system and flow exergy terms also arise naturally. The result is an enhanced teaching and learning strategy that exemplifies a rigorous approach and emphasizes the scope and rigor of thermodynamics.
The proposed paper will support a rigorous derivation and presentation of the FEE. The result supports a brief presentation that can be conducted in class without an excessive investment in time or be readily packaged into a video presentation for student-paced self-study. Ultimately, this presentation should be a useful addition to an elementary or intermediate thermodynamics course or any thermal and energy systems engineering course.

AU - Sheldon Jeter
CY - Minneapolis, MN
DA - 2022/08/23
PB - ASEE Conferences
TI - Rigorous Development of the Fixed Dead State Version of the Exergy Equation Suitable for Undergraduate Class Presentation and Coursework
UR - https://peer.asee.org/41325
DO - 10.18260/1-2--41325
ER -