Maximum efficiency of solar energy conversion Wongee Chun 1 , Seung Jin Oh 1 , Sang Hoon Lim 2 and Kuan Chen 3, * ,† 1 Department of Nuclear and Energy Engineering, Cheju National University, Cheju, Korea 2 New & Renewable Energy Research Division, Korea Institute of Energy Research, Daejeon, Korea 3 Department of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA SUMMARY Owing to the energy scattered or absorbed by the constituents of earth’s atmosphere and self-absorption in the outer layers of the sun, the spectrum of solar flux at earth’s surface is different from that of a blackbody. Consequently, the second law of thermodynamics for heat engine cycles operating between thermal reservoirs needs to be revised to determine the max- imum conversion efficiency. A thermodynamic model similar to those for multi-temperature plasmas and non-isothermal particle-exchange heat engines is proposed to estimate the maximum conversion efficiency of a mechanical or solid-state heat engine subject to a radiation flux not having a blackbody spectrum. An example is given to illustrate the calculation of the maximum power that can be converted from a solar flux with considerable gas absorption. Copyright © 2011 John Wiley & Sons, Ltd. KEY WORDS conversion efficiency; solar energy Correspondence *Kuan Chen, MEB 2130, 50 S. Central Campus Drive, SLC, UT 84112, USA. † E-mail: chen@mech.utah.edu Received 2 May 2011; Revised 13 July 2011; Accepted 16 July 2011 1. INTRODUCTION Recent surges in energy costs and concerns about global warming have stimulated significant interest in and atten- tion on renewable and sustainable energy such as solar, wind, geothermal, and oceanic energy. Among these en- ergy sources, solar energy is probably the most convenient to use. Solar cells that employed the photovoltaic (PV) technology have been commonly installed on building roofs and in gardens or other open spaces to directly con- vert solar energy into electricity. Concentrated solar energy collected by lenses or curved mirrors and sun-tracking devices also have been used to generate electricity by means of high-efficiency solar cells or mechanical heat engines such as steam turbines or Stirling engines. Other designs and devices that can directly convert solar energy into electricity or mechanical power include thermionic engines and thermoelectric couples. At present, PV seems to be the most promising technol- ogy to economically and efficiently convert solar energy into electrical power in the future. A computational proce- dure was outlined in White’s paper [1] for comparing alternative solar energy conversion processes. The proce- dure was illustrated in this paper by comparisons of PV converters of different designs and efficiencies. Flexible substrates have been developed in recent years to re- place glass substrates for large-volume and cost-efficient manufacturing of solar cells [2]. Early PV panels have con- version efficiencies below 10%. Later use of multi-junction cell designs and GaInAs and other advanced materials in conjunction with concentrated solar flux had boosted the PV conversion efficiency to above 30% [3]. The perfor- mance of solar cells is wavelength dependent. By incorpo- rating new semiconductor layers that excel at capturing solar energy in the infrared range, researchers at Spectrolab and NREL converted more than 40% of concentrated solar energy into electricity in 2007 [4]. In the same year, researchers at Delaware University reached a conversion efficiency of 42.8% [5] at standard terrestrial conditions. This new PV technology not only has a thermal efficiency comparable to those of conventional heat engines (e.g., the diesel engine), but it does not require concentrated solar energy. As a result, expensive and sophisticated collector designs and sun-tracking systems are not needed for this new PV design. As the race of efficient solar energy converters heats up, one question is naturally raised: what is the highest conver- sion efficiency these solar energy converters can attain? According to the second law of thermodynamics (more specifically, the Kelvin–Planck statement and the Carnot INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1922 Copyright © 2011 John Wiley & Sons, Ltd.