Effect of temperature-dependent energy levels on exergy

The performances of solar cells and thermoelectricmaterials are governed by thermodynamics. The material properties of these have temperature dependence due to thermal expansions of lattices and an effect of electron–phonon coupling etc. The temperature-dependent energy levels has been included in statisticalmechanics, naturally requiring a rectification of the second law of thermodynamics with an effective heat. In such a framework, we show that exergy associatedwith internal energy of isolated systems can be increased in irreversible processes.We furthermore see how the effect of the temperature-dependent energy levels appears in the thermodynamic performance in terms of the second law efficiency.