Exergy destruction is minimized when the process is reversible, i.e., when entropy generation (S_gen) is zero. Per Gouy-Stodola theorem, X_destroyed = T₀ × S_gen, so S_gen = 0 implies no exergy destruction.

For a steady-flow system, the specific flow exergy is x = (h – h₀) – T₀(s – s₀), where h and s are the enthalpy and entropy of the stream, and h₀, s₀ are at the dead state. For mass flow rate ṁ, X = ṁ x

 Maximum work (exergy) = Q [1 – (T₀/T)] = 500 [1 – (300/400)] = 500 × 0.25 = 125 kJ, where T₀ = 300 K and T = 400 K.

 Exergy destruction occurs due to irreversibilities (e.g., friction, heat transfer across finite temperature differences) and is always positive, as per Gouy-Stodola theorem: X_destroyed = T₀ × S_gen, where S_gen > 0.

 Second law efficiency (η₂) is the ratio of the exergy recovered (or useful exergy output) to the exergy supplied, reflecting how effectively a process utilizes available work.

 Exergy loss = Q [1 – (T₀/T)] = 1000 [1 – (300/500)] = 1000 × 0.4 = 400 kJ, where T₀ = 300 K is the surroundings temperature and T = 500 K is the reservoir temperature.

 The exergy of a closed system is X = (U – U₀) + P₀(V – V₀) – T₀(S – S₀), where U, V, S are the system’s internal energy, volume, and entropy, and U₀, V₀, S₀ are the corresponding values at the dead state (P₀, T₀).

 At the dead state (equilibrium with the surroundings), the system has no potential to do work, so its exergy is zero.

Anergy is the part of the total energy that is unavailable for conversion into useful work, often associated with losses due to irreversibilities or heat transfer to the surroundings.

 Exergy is the maximum theoretical useful work (shaft work or electrical work) obtainable from a system as it reaches equilibrium with its surroundings (dead state).