Energy conversion processes inherently have associated irreversibility. A better understanding of energy conversion will motivate intuition to create new energy-conversion and energy-utilization technology. In the present article, such understanding is further enhanced by decomposing the equations of energy and exergy (availability, available energy, useful energy) to reveal the reversible and irreversible parts of energy transformations. New definitions of thermal, strain, chemical, mechanical and thermochemical forms of energy/exergy are justified and expressions for these properties and their changes are rigorously developed. In the resulting equations, terms appear which explicitly reveal the interconversions between the different forms of energy/exergy, including the breakdown into reversible and irreversible conversions. The equations are valid for chemically reacting or non-reacting inelastic fluids, with or without diffusion.