{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,26]],"date-time":"2026-10-26T11:02:01Z","timestamp":1793012521720,"version":"4.5.0"},"reference-count":58,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T00:00:00Z","timestamp":1761436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Exergy efficiency is a measure of thermodynamic perfection. A device that operates reversibly has an exergy efficiency of 100 percent and is said to be thermodynamically perfect. A reversible process involves zero entropy generation and thus zero exergy destruction since Xdestroyed = T0Sgen. Exergy efficiency is generally defined as the ratio of exergy output to exergy input \u03b7ex = Xoutput\/Xinput = 1 \u2212 (Xdestroyed + Xloss)\/Xinput or the ratio of exergy recovered to exergy expended \u03b7ex = Xrecovered\/Xexpended = 1 \u2212 Xdestroyed\/Xexpended. In this paper, exergy efficiency relations are obtained first for a general steady-flow system using both approaches. Then, explicit general relations are obtained for common steady-flow devices, such as turbines, compressors, pumps, nozzles, diffusers, valves and heat exchangers, as well as heat engines, refrigerators, and heat pumps. For power and refrigeration cycles, five different forms of exergy efficiency relations are developed, and their equivalence is demonstrated. With the unified approach presented here and the insights provided, the controversy and confusion associated with different exergy efficiency definitions are largely alleviated.<\/jats:p>","DOI":"10.3390\/e27111108","type":"journal-article","created":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T00:51:42Z","timestamp":1761526302000},"page":"1108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Systematic Approach to Exergy Efficiency of Steady-Flow Systems"],"prefix":"10.3390","volume":"27","author":[{"given":"Yunus A.","family":"\u00c7engel","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehmet","family":"Kano\u011flu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Alanya Alaaddin Keykubat University, Antalya 07425, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,26]]},"reference":[{"key":"ref_1","unstructured":"\u00c7engel, Y.A., Boles, M.A., and Kano\u011flu, M. (2024). Thermodynamics: An Engineering Approach, McGraw-Hill. [10th ed.]."},{"key":"ref_2","unstructured":"Moran, M.J., Shapiro, H.N., Boettner, D.D., and Bailey, M.B. (2024). Fundamentals of Engineering Thermodynamics, Wiley. [9th ed.]."},{"key":"ref_3","unstructured":"Borgnakke, C., and Sonntag, R.E. (2017). Fundamentals of Thermodynamics, Wiley. [9th ed.]."},{"key":"ref_4","unstructured":"Bejan, A., Tsatsaronis, G., and Moran, M.J. (1995). Thermal Design and Optimization, Wiley."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bejan, A. (2016). Advanced Engineering Thermodynamics, John Wiley & Sons.","DOI":"10.1002\/9781119245964"},{"key":"ref_6","unstructured":"Kotas, T.J. (1985). The Exergy Method of Thermal Plant Analysis, Butterworths."},{"key":"ref_7","unstructured":"Szargut, J., Morris, D.R., and Steward, F.R. (1988). Exergy Analysis of Thermal, Chemical and Metallurgical Processes, Hemisphere."},{"key":"ref_8","unstructured":"Szargut, J. (2005). Exergy Method: Technical and Ecological Applications, WIT Press."},{"key":"ref_9","unstructured":"Wark, K. (1988). Thermodynamics, McGraw-Hill. [5th ed.]."},{"key":"ref_10","unstructured":"Moran, M.J. (1989). Availability Analysis: A Guide to Efficient Energy Use, Prentice-Hall."},{"key":"ref_11","first-page":"36","article-title":"Exergie, ein neues Wort f\u00fcr \u201ctechnische Arbeitsf\u00e4higkeit\u201d (Exergy, a new word for \u2018technical work capacity\u2019)","volume":"22","author":"Rant","year":"1956","journal-title":"Forsch. Ing. Wes."},{"key":"ref_12","first-page":"1","article-title":"A brief commented history of exergy from the beginnings to 2004","volume":"10","author":"Sciubba","year":"2007","journal-title":"Int. J. Thermodyn."},{"key":"ref_13","unstructured":"Cornelissen, R.L. (1997). Thermodynamics and Sustainable Development: The Use of Exergy Analysis and the Reduction of Irreversibility. [Ph.D. Thesis, University of Twente]."},{"key":"ref_14","unstructured":"Brodyansky, V.M., Sorin, M.V., and Le Goff, P. (1994). The Efficiency of Industrial Processes: Exergy Analysis and Optimization, Elsevier Science B.V."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.energy.2006.01.019","article-title":"Energy, exergy, and Second Law performance criteria","volume":"32","author":"Lior","year":"2007","journal-title":"Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.energy.2012.06.001","article-title":"A comparison of exergy efficiency definitions with focus on low temperature processes","volume":"44","author":"Gundersen","year":"2012","journal-title":"Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.energy.2014.06.020","article-title":"On the definition of exergy efficiencies for petroleum systems: Application to offshore oil and gas processing","volume":"73","author":"Nguyen","year":"2014","journal-title":"Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.energy.2017.09.137","article-title":"An experimental study of combustion, performance, exergy and emission characteristics of a CI engine fueled by Diesel-ethanol-biodiesel blends","volume":"141","author":"Paul","year":"2017","journal-title":"Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"122565","DOI":"10.1016\/j.energy.2021.122565","article-title":"Thermodynamic analyses of a modified ejector enhanced dual temperature refrigeration cycle for domestic refrigerator\/freezer application","volume":"244","author":"Chen","year":"2022","journal-title":"Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"123579","DOI":"10.1016\/j.energy.2022.123579","article-title":"Exergy and thermoeconomic analyses of the diffusion absorption refrigeration system with various nanoparticles and their different ratios as work fluid","volume":"248","author":"Gurbuz","year":"2022","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"126142","DOI":"10.1016\/j.energy.2022.126142","article-title":"Exergy assessment and sustainability of a simple off-shore oscillating water column device","volume":"264","author":"Quiros","year":"2023","journal-title":"Energy"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"132854","DOI":"10.1016\/j.energy.2024.132854","article-title":"Stage-based exergy analysis for a modern turboprop engine under various loading","volume":"308","author":"Kirmizi","year":"2024","journal-title":"Energy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/S0375-6505(02)00032-9","article-title":"Exergy analysis of a dual-level binary geothermal power plant","volume":"31","author":"Kanoglu","year":"2002","journal-title":"Geothermics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/er.814","article-title":"Exergy analysis of multistage cascade refrigeration cycle used for natural gas liquefaction","volume":"26","author":"Kanoglu","year":"2002","journal-title":"Int. J. Energy Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"115002","DOI":"10.1016\/j.enconman.2021.115002","article-title":"Effects of process-thermal configuration on energy, exergy, and thermo-economic performance of solar driven supercritical water gasification","volume":"251","author":"Onigbajumo","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.enconman.2016.02.029","article-title":"Exergetic and exergoeconomic analysis of a novel hybrid solar-geothermal polygeneration system producing energy and water","volume":"115","author":"Calise","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"113914","DOI":"10.1016\/j.enconman.2021.113914","article-title":"Thermodynamic analysis and comparative investigation of a new combined heating and power system driving by medium-and-high temperature geothermal water","volume":"233","author":"Ren","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.enconman.2015.11.048","article-title":"Exergic, economic and environmental impacts of natural gas and diesel in operation of combined cycle power plants","volume":"109","author":"Vandani","year":"2016","journal-title":"Energy Convers. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.enconman.2016.12.020","article-title":"New exergy analysis of a regenerative closed Brayton cycle","volume":"134","author":"Naserian","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"112062","DOI":"10.1016\/j.enconman.2019.112062","article-title":"Integration of reversible absorption heat pumps in cogeneration systems: Exergy and economic assessment","volume":"200","author":"Urbanucci","year":"2019","journal-title":"Energy Convers. Manag."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hu, Z., de Le\u00f3n, F., Wang, R., and Li, Y. (2023). Effects of Installing Different Types of Cooling Fins on the Cold Side of a Thermoelectric Power Generation Device on the Thermal Efficiency and Exergy Efficiency of Power Cable Surface Waste Heat Recovery. Micromachines, 14.","DOI":"10.3390\/mi14081591"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Br\u00f6tz, J., Schanzle, C., and Pelz, P.F. (2023). Exergy-based efficiency assessment of fans vs. isentropic efficiency. Int. J. Turbomach. Propuls. Power, 8.","DOI":"10.3390\/ijtpp8010004"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zulkefal, M., Ayub, A., and Sethi, H. (2024). Exergy analysis of methanol production plant from hydrogenation of carbon dioxide. Mater. Proc., 17.","DOI":"10.3390\/materproc2024017015"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Hecht, K., Reboso, A.O., van der Vegt, M., Appelman, J., and Zari, M.P. (2024). Ecologically regenerative building systems through exergy efficiency: Designing for structural order and ecosystem services. Land, 13.","DOI":"10.3390\/land13091375"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Wang, Z., Wang, H., Zhu, H., and Xiong, W. (2023). Conventional and Advanced Exergy Analyses of Industrial Pneumatic Systems. Energies, 16.","DOI":"10.3390\/en16165982"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1016\/j.applthermaleng.2016.11.142","article-title":"Exergoeconomic analysis of integrated natural gas liquids (NGL) and liquefied natural gas (LNG) processes","volume":"113","author":"Ghorbani","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.applthermaleng.2015.01.076","article-title":"Optimisation processes of energy efficiency for a drying plant: A case of study for Turkey","volume":"80","author":"Taner","year":"2015","journal-title":"Appl. Therm. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.applthermaleng.2008.02.029","article-title":"Energy and exergy analysis of a steam power plant in Jordan","volume":"29","author":"Aijundi","year":"2009","journal-title":"Appl. Therm. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2560","DOI":"10.1016\/j.apenergy.2009.04.005","article-title":"Comprehensive exergy analysis of a ground-source heat pump system for both building heating and cooling modes","volume":"86","author":"Bi","year":"2009","journal-title":"Appl. Energy"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Xu, K., Qi, Y., Sun, C., Ai, D., Wang, J., He, W., Yang, F., and Ren, H. (2024). Exergy Flow as a Unifying Physical Quantity in Applying Dissipative Lagrangian Fluid Mechanics to Integrated Energy Systems. Entropy, 26.","DOI":"10.3390\/e26090791"},{"key":"ref_41","unstructured":"Wall, G. (1977). Exergy-A Useful Concept Within Resource Accounting, Institute of Theoretical Physics, Chalmers University of Technology and University of G\u00f6teborg. Report no. 77-42."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Righetto, F.G., and Mady, C.E.K. (2023). Exergy Analysis of a Sugarcane Crop: A Planting-to-Harvest Approach. Sustainability, 15.","DOI":"10.3390\/su152014686"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1016\/j.enconman.2008.02.012","article-title":"First and second law analysis of diesel engine powered cogeneration systems","volume":"49","author":"Abusoglu","year":"2008","journal-title":"Energy Convers. Manag."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3967","DOI":"10.1016\/j.enpol.2007.01.015","article-title":"Understanding energy and exergy efficiencies for improved energy management in power plants","volume":"35","author":"Dincer","year":"2007","journal-title":"Energy Policy"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.enpol.2007.09.006","article-title":"Role of exergy in increasing efficiency and sustainability and reducing environmental impact","volume":"36","author":"Rosen","year":"2008","journal-title":"Energy Policy"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1016\/j.applthermaleng.2003.10.003","article-title":"Energy and Exergy Analyses of an Experimental Open-Cycle Desiccant Cooling System","volume":"24","year":"2004","journal-title":"Appl. Therm. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Wang, D., Zhang, X., Zhu, Y., and Jiang, Z. (2024). Optimization of Exergy Efficiency in a Walking Beam Reheating Furnace Based on Numerical Simulation and Entropy Generation Analysis. Processes, 12.","DOI":"10.3390\/pr12030451"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1243\/09576500360611399","article-title":"Exergy tools","volume":"217","author":"Wall","year":"2003","journal-title":"Proc. Inst. Mech. Eng. Part A J. Power Energy"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3989","DOI":"10.1002\/er.4123","article-title":"Exergy-based performance indicators for industrial practice","volume":"42","author":"Magnanelli","year":"2018","journal-title":"Int. J. Energy Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1016\/0360-5442(93)90006-Y","article-title":"Theory of exergetic cost","volume":"18","author":"Lozano","year":"1993","journal-title":"Energy"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/j.energy.2005.03.011","article-title":"SPECO: A systematic and general methodology for calculating efficiencies and costs in thermal systems","volume":"31","author":"Lazzaretto","year":"2006","journal-title":"Energy"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0306-2619(89)90016-0","article-title":"Chemical exergies of the elements","volume":"32","author":"Szargut","year":"1989","journal-title":"Appl. Energy"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.energy.2006.07.002","article-title":"Definitions and nomenclature in exergy analysis and exergoeconomics","volume":"32","author":"Tsatsaronis","year":"2007","journal-title":"Energy"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1002\/er.804","article-title":"Fundamentals of exergy analysis, entropy-generation minimization and the generation of flow architecture","volume":"26","author":"Bejan","year":"2002","journal-title":"Int. J. Energy Res."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"\u00c7engel, Y.A., and Kano\u011flu, M. (2025). Exergy Efficiency of Closed and Unsteady-Flow Systems. Entropy, 27.","DOI":"10.3390\/e27090943"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"116","DOI":"10.3390\/e3030116","article-title":"Energy, entropy and exergy concepts and their roles in thermal engineering","volume":"3","author":"Dincer","year":"2001","journal-title":"Entropy"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.rser.2006.10.001","article-title":"A key review on exergetic analysis and assessment of renewable energy resources for a sustainable future","volume":"12","author":"Hepbasli","year":"2008","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_58","unstructured":"(2025). Engineering Equation Solver (EES) Software, F-Chart Software. Version 10."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T02:26:46Z","timestamp":1761704806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1108"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,26]]},"references-count":58,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["e27111108"],"URL":"https:\/\/doi.org\/10.3390\/e27111108","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,26]]}}}