This paper proposes a clear path to the exergy balance by subtracting the second Law balance (multiplied by Ta) to the first Law that let appear all the exergy terms. In each exergy terms it is shown that it is essential to clearly distinguish the process-dependent entities from the state functions and how the latter can be visualized in parametric representations including 3D. An opportunity is shown to superpose the various dead states (thermo-mechanical or physicochemical equilibrium). The typical First Law indicators (Effectiveness, coefficient of performance) are compared with the corresponding exergy efficiency for integrated processes including house heating with cogeneration and heat pumps or the valorization of LNG evaporation. From this strong basis the development of both First Law and Exergy efficiencies is shown for a variety of systems providing different energy services in the whole range of temperatures. A much greater coherence of the exergy approach for modern systems including co-or tri-generation is highlighted. The power of the notion of exergy efficiency is further illustrated by comparing various heating or air-conditioning energy systems in urban areas with the possibility to multiply the exergy efficiency of the subsystems to get a coherent ranking of the active technology options. Ultimately, we briefly show how one specific emerging platform (nolej) based on AI could simplify the work of teachers in thermodynamics in general.