{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:30:53Z","timestamp":1760146253318,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deutsche Forschungsgemeinschaft","award":["KA 1211\/32-1"],"award-info":[{"award-number":["KA 1211\/32-1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, the transported entropy of ions for 8YSZ and 10Sc1CeSZ electrolytes was experimentally determined to enable precise modeling of heat transport in solid oxide cells (SOCs). The Peltier coefficient, crucial for thermal management, was directly calculated, highlighting reversible heat transport effects in the cell. While data for 8YSZ are available in the literature, providing a basis for comparison, the results for 10Sc1CeSZ show slightly smaller Seebeck coefficients but higher transported ion entropies. Specifically, at 700\u00b0C and an oxygen partial pressure of pO2=0.21 bar, values of SO2\u2212*=52\u00b110 J\/K\u00b7F for 10Sc1CeSZ and SO2\u2212*=48\u00b19 J\/K\u00b7F for 8YSZ were obtained. The transported entropy was also validated through theoretical calculations and showed minimal deviations when comparing different cell operation modes (O2||O2\u2212||O2 and H2, H2O||O2\u2212||O2). The influence of the transported entropy of the ions on the total heat generation and the partial heat generation at the electrodes is shown. The temperature has the greatest influence on heat generation, whereby the ion entropy also plays a role. Finally, the Peltier coefficients of 8YSZ for all homogeneous phases agree with the literature values.<\/jats:p>","DOI":"10.3390\/e26100872","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T11:19:18Z","timestamp":1729163958000},"page":"872","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Transported Entropy of Ions and Peltier Coefficients in 8YSZ and 10Sc1CeSZ Electrolytes for Solid Oxide Cells"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7087-1299","authenticated-orcid":false,"given":"Aydan","family":"Gedik","sequence":"first","affiliation":[{"name":"Institute of Thermodynamics, Leibniz University Hannover, Welfengarten 1, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1616-1402","authenticated-orcid":false,"given":"Stephan","family":"Kabelac","sequence":"additional","affiliation":[{"name":"Institute of Thermodynamics, Leibniz University Hannover, Welfengarten 1, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115899","DOI":"10.1016\/j.apenergy.2020.115899","article-title":"A review of heat transfer and thermal management methods for temperature gradient reduction in solid oxide fuel cell (SOFC) stacks","volume":"280","author":"Zeng","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kjelstrup Ratkje, S., Bedeaux, D., Johannessen, E., and Gross, J. (2017). Non-Equilibrium Thermodynamics for Engineers, World Scientific. [2nd ed.].","DOI":"10.1142\/10286"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gedik, A., Lubos, N., and Kabelac, S. (2022). Coupled Transport Effects in Solid Oxide Fuel Cell Modeling. Entropy, 24.","DOI":"10.3390\/e24020224"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"014501","DOI":"10.1149\/2754-2734\/ad1a73","article-title":"Comparative Analysis of Loss Mechanism Localization in a Semi-2D SOEC Single Cell Modell: Non-Equilibrium Thermodynamics versus Monocausal-Based Approach","volume":"3","author":"Gedik","year":"2024","journal-title":"ECS Adv."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.electacta.2015.09.059","article-title":"Seebeck coefficients of cells with lithium carbonate and gas electrodes","volume":"182","author":"Kang","year":"2015","journal-title":"Electrochim. Acta"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.electacta.2015.09.059","article-title":"Seebeck coefficients of cells with molten carbonates relevant for the metallurgical industry","volume":"182","author":"Kang","year":"2015","journal-title":"Electrochim. Acta"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Barrag\u00e1n, V.M., Kristiansen, K.R., and Kjelstrup, S. (2018). Perspectives on Thermoelectric Energy Conversion in Ion-Exchange Membranes. Entropy, 20.","DOI":"10.3390\/e20120905"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"044037","DOI":"10.1103\/PhysRevApplied.11.044037","article-title":"Thermoelectric Power of Ion Exchange Membrane Cells Relevant to Reverse Electrodialysis Plants","volume":"11","author":"Kristiansen","year":"2019","journal-title":"Phys. Rev. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"020901","DOI":"10.1063\/5.0131731","article-title":"Seebeck, Peltier, and Soret effects: On different formalisms for transport equations in thermogalvanic cells","volume":"158","author":"Kjelstrup","year":"2023","journal-title":"J. Chem. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"050522","DOI":"10.1149\/1945-7111\/abfd73","article-title":"Review\u2014Reversible Heat Effects in Cells Relevant for Lithium-Ion Batteries","volume":"168","author":"Gunnarshaug","year":"2021","journal-title":"J. Electrochem. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1016\/0013-4686(87)85070-3","article-title":"Single electrode peltier heat of a hydrogen electrode in H2SO4 and NaOH solutions","volume":"32","author":"Kamata","year":"1987","journal-title":"Electrochim. Acta"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1149\/1.2054902","article-title":"Theory of Thermocells: Transported Entropies, and Heat of Transfer in Sulfate Mixtures","volume":"141","author":"Grimstvedt","year":"1994","journal-title":"J. Electrochem. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/0376-7388(95)00117-7","article-title":"Thermoelectric power relevant for the solid-polymer-electrolyte fuel cell","volume":"107","author":"Ratkje","year":"1995","journal-title":"J. Membr. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"E364","DOI":"10.1149\/1.1386642","article-title":"The Role of the Transported Entropy of Lead Ions in Partially Thermostated and Adiabatic Cells","volume":"148","author":"Blinov","year":"2001","journal-title":"J. Electrochem. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.tca.2008.04.002","article-title":"The electrochemical Peltier heat of the standard hydrogen electrode reaction","volume":"473","author":"Fang","year":"2008","journal-title":"Thermochim. Acta"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.electacta.2013.03.045","article-title":"The Seebeck coefficient and the Peltier effect in a polymer electrolyte membrane cell with two hydrogen electrodes","volume":"99","author":"Kjelstrup","year":"2013","journal-title":"Electrochim. Acta"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"100040","DOI":"10.1016\/j.cpletx.2019.100040","article-title":"The heat of transfer and the Peltier coefficient of electrolytes","volume":"738","author":"Gunnarshaug","year":"2020","journal-title":"Chem. Phys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1149\/1.2428586","article-title":"Measurements on Galvanic Cells Involving Solid Electrolytes","volume":"104","author":"Kiukkola","year":"1957","journal-title":"J. Electrochem. Soc."},{"key":"ref_19","first-page":"572","article-title":"\u00dcber Zirkondioxyd als Elektrolyt f\u00fcr elektrochemische Untersuchungen bei h\u00f6heren Temperaturen","volume":"66","author":"Schmalzried","year":"1962","journal-title":"Z. F\u00fcr Elektrochem. Berichte Der Bunsenges. F\u00fcr Phys. Chem."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1149\/1.2426149","article-title":"Transport Numbers in Stabilized Zirconia","volume":"111","author":"Bray","year":"1964","journal-title":"J. Electrochem. Soc."},{"key":"ref_21","first-page":"1359","article-title":"Factors influencing the performance of solid oxide electrolytes in high temperature thermodynamic measurements","volume":"233","author":"Steele","year":"1965","journal-title":"Trans. Met. Soc. AIME"},{"key":"ref_22","first-page":"212","article-title":"Solid electrolytes for use at steelmaking temperatures","volume":"204","author":"Baker","year":"1966","journal-title":"J. Iron Steel Inst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fischer, W.A., and Janke, D. (1972). Die Anwendbarkeit von ZrO2-Y2O3-, ZrO2-CaO- und ThO2-Y2O3-Festelektrolyten bei 1000 bis 1600 \u00b0C, VS Verlag f\u00fcr Sozialwissenschaften.","DOI":"10.1007\/978-3-663-06805-1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1002\/srin.197304526","article-title":"Die elektrische Leitf\u00e4higkeit und Thermokraft von reinem und mit Calciumoxid stabilisiertem Zirkonoxid bei Temperaturen zwischen 1000 und 1700 \u00b0C und Sauerstoffpartialdr\u00fccken zwischen 1 und 10\u201316 atm","volume":"44","author":"Fischer","year":"1973","journal-title":"Arch. F\u00fcr Das Eisenh\u00fcttenwesen"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1149\/1.2096302","article-title":"Electronic Transport in 8 Mole Percent Y2O3\u2013ZrO2","volume":"136","author":"Park","year":"1989","journal-title":"J. Electrochem. Soc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/S0167-2738(02)00382-X","article-title":"Nonstoichiometry and electrical transport in Sc-doped zirconia","volume":"152\u2013153","author":"Kosacki","year":"2002","journal-title":"Solid State Ionics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/S0031-8914(53)80124-2","article-title":"On the theory of thermocouples and thermocells","volume":"19","author":"Holtan","year":"1953","journal-title":"Physica"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0167-2738(95)00201-3","article-title":"Thermoelectric power of stabilized zirconia","volume":"82","author":"Ahlgren","year":"1995","journal-title":"Solid State Ionics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1515\/zna-1967-1019","article-title":"Die Thermokraft von kubisch stabilisiertem Zirkonoxid zwischen Sauerstoffelektroden","volume":"22","author":"Fischer","year":"1967","journal-title":"Z. F\u00fcr Naturforschung A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1149\/1.2411290","article-title":"Seebeck Coefficient of a (ZrO2)0.85 (CaO)0.15 Electrolyte Thermocell","volume":"115","author":"Ruka","year":"1968","journal-title":"J. Electrochem. Soc."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1515\/zna-1970-0410","article-title":"On the Thermoelectric Power of Stabilized Zirconia","volume":"25","author":"Pizzini","year":"1970","journal-title":"Z. F\u00fcr Naturforschung A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1016\/0022-3697(92)90126-X","article-title":"Thermoelectric behavior of single crystalline ZrO2(+8mo Y2O3)","volume":"53","author":"Yoo","year":"1992","journal-title":"J. Phys. Chem. Solids"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/0013-4686(93)85164-T","article-title":"Exergy effeciency and local heat production in solid oxide fuel cells","volume":"38","author":"Ratkje","year":"1993","journal-title":"Electrochim. Acta"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2506","DOI":"10.1149\/1.2097448","article-title":"Thermal Energy Generated by Entropy Change in Solid Oxide Fuel Cell","volume":"136","author":"Takehara","year":"1989","journal-title":"J. Electrochem. Soc."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2374","DOI":"10.1149\/1.2085979","article-title":"The Transported Entropy of Oxygen Ion in Yttria\u2013Stabilized Zirconia","volume":"138","author":"Ratkje","year":"1991","journal-title":"J. Electrochem. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2165","DOI":"10.1149\/1.2085944","article-title":"Dependence of Entropy Change of Single Electrodes on Partial Pressure in Solid Oxide Fuel Cells","volume":"138","author":"Kanamura","year":"1991","journal-title":"J. Electrochem. Soc."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"011002","DOI":"10.1115\/1.2971042","article-title":"Location and Magnitude of Heat Sources in Solid Oxide Fuel Cells","volume":"6","author":"Fischer","year":"2009","journal-title":"J. Fuel Cell Sci. Technol."},{"key":"ref_38","unstructured":"Nguyen, Q.M., and Takahashi, T. (1995). Science and Technology of Ceramic Fuel Cells, Elsevier Science."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.matpr.2018.10.071","article-title":"Properties of 10Sc1CeSZ-3.5YSZ(33-, 40-, 50-wt.%) Composite Ceramics for SOFC Application","volume":"6","author":"Brodnikovskyi","year":"2019","journal-title":"Mater. Today Proc."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kjelstrup, S., and Bedeaux, D. (2008). Non-Equilibrium Thermodynamics of Heterogeneous Systems, World Scientific.","DOI":"10.1142\/9789812779144"},{"key":"ref_41","unstructured":"Forland, K.S., Forland, T., and Ratkje, S.K. (1988). Irreversible Thermodynamics: Theory and Applications, John Wiley & Sons."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Kjelstrup, S., Bedeaux, D., Johannessen, E., and Gross, J. (2010). Non-Equilibrium Thermodynamics for Engineers, World Scientific.","DOI":"10.1142\/7869"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1063\/1.1662324","article-title":"Absolute Seebeck coefficient of platinum from 80 to 340 K and the thermal and electrical conductivities of lead from 80 to 400 K","volume":"44","author":"Moore","year":"1973","journal-title":"J. Appl. Phys."},{"key":"ref_44","first-page":"25","article-title":"Heat Mass and Charge Transport and Chemical Reactions at Surfaces","volume":"8","author":"Bedeaux","year":"2005","journal-title":"Int. J. Thermodyn."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s10010-005-0016-y","article-title":"Thermodynamische Stoffdaten f\u00fcr Biogase","volume":"70","author":"Kabelac","year":"2005","journal-title":"Forsch. Ingenieurwesen"},{"key":"ref_46","unstructured":"International Organization for Standardization (2008). ISO\/IEC Guide 98-3:2008: Uncertainty of Measurement\u2014Part 3: Guide to the Expression of Uncertainty in Measurement (GUM), ISO. Available online: https:\/\/www.iso.org\/standard\/50461.html."},{"key":"ref_47","unstructured":"(2014). DIN EN 60584-1:2014-07. Thermoelemente_- Teil_1: Thermospannungen und Grenzabweichungen (IEC_60584-1:2013), DIN Media GmbH. Deutsche Fassung EN_60584-1:2013."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/0167-2738(94)90366-2","article-title":"Thermoelectric power of YSZ","volume":"70\u201371","author":"Ahlgren","year":"1994","journal-title":"Solid State Ionics"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/10\/872\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:15:30Z","timestamp":1760112930000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/10\/872"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,17]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["e26100872"],"URL":"https:\/\/doi.org\/10.3390\/e26100872","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,10,17]]}}}