| name | exergy-analysis |
| description | Exergy (availability) analysis — exergy of heat/work/streams, exergy destruction, second-law efficiency, exergy balance, pinch analysis, Gouy-Stodola theorem. |
| metadata | {"priority":7,"promptSignals":{"phrases":["exergy","availability","second law efficiency","exergy destruction","irreversibility","Gouy-Stodola"],"minScore":3}} |
Exergy Analysis — Complete Skill
Definitions
Exergy
Maximum useful work extractable from a system interacting with the dead state (T₀, P₀)
Dead state: T₀ = 298 K (25°C), P₀ = 101.325 kPa (standard atmosphere)
Physical exergy of flow stream:
ex_ph = (h - h₀) - T₀(s - s₀)
h, s = specific enthalpy and entropy at state
h₀, s₀ = dead state values
Chemical exergy (not covered in basic analysis): accounts for composition differences from dead state
Exergy of Heat and Work
Exergy of Heat Transfer
Ex_Q = Q × (1 - T₀/T) [Carnot factor × Q]
At T > T₀: Ex_Q > 0 (valuable heat)
At T < T₀ (refrigeration): Ex_Q = Q × (T₀/T - 1) > 0 (must do work to transfer to lower T)
Exergy of Work
Ex_W = W (work is 100% exergy)
Exergy of a Stream
Ẋ = ṁ × ex = ṁ × [(h - h₀) - T₀(s - s₀)]
Ideal gas:
ex_ph = c_p(T - T₀) - T₀[c_p ln(T/T₀) - R ln(P/P₀)]
Exergy Balance (Control Volume)
General Exergy Balance
dX_CV/dt = Σ Ẋ_Q,j - Ẇ_useful + Σ ṁ_in ex_in - Σ ṁ_out ex_out - Ẋ_destroyed
Steady state:
Ẋ_destroyed = Σ(Ẋ_Q,in) + Ẇ_in + Σ(ṁ_in ex_in) - Σ(ṁ_out ex_out) - Ẇ_out ≥ 0
Gouy-Stodola Theorem:
Ẋ_destroyed = T₀ × Ṡ_gen [irreversibility proportional to entropy generation]
Second-Law Efficiency
Definition
η_II = (Exergy output) / (Exergy input) = 1 - Ẋ_destroyed / Ẋ_input
vs. First-law efficiency:
η_I = (Energy output) / (Energy input) — ignores quality
η_II = (Exergy output) / (Exergy input) — accounts for quality
Component Efficiencies
Heat exchanger: η_II = ΔẊ_cold / ΔẊ_hot (exergy gained by cold / exergy lost by hot)
Compressor: η_II = Ẋ_isentropic / Ẇ_actual = (h₂s - h₁ - T₀(s₂s-s₁)) / Ẇ_shaft
Turbine: η_II = Ẇ_actual / Ẋ_isentropic
Exergy Destruction — Key Sources
Ranking by Source
- Combustion: irreversible chemical reaction → large Ṡ_gen (accounts for 20-30% of fuel exergy)
ex_combustion_loss = T₀ × Q_comb/T_flame × ...
- Heat transfer over ΔT: Ẋ_destroyed = Q × T₀ × (1/T_cold - 1/T_hot)
- Friction (pressure drop): Ẋ_destroyed = ṁ T₀ (s₂ - s₁) ≈ ṁ T₀ Δh/T_avg × ...
- Mixing of streams: irreversible unless reversible mixing device used
Minimize Ẋ_destroyed by:
- Reducing ΔT in heat exchangers (increase area)
- Reducing pressure drop (increase pipe size, use smooth bends)
- Staging combustion at multiple temperatures
Pinch Analysis
Minimum energy consumption in process integration:
Hot composite curve + cold composite curve in T-H diagram
Pinch point: minimum temperature approach ΔT_min (e.g., 10-20°C)
Minimum hot utility: Q_H,min = area above pinch (hot streams cannot heat cold streams across pinch)
Minimum cold utility: Q_C,min = area below pinch
Rules:
- Never transfer heat across the pinch
- No hot utility below the pinch
- No cold utility above the pinch
Application — Power Plant
Typical exergy destruction breakdown for coal power plant (η_I = 35%):
- Combustion: 30% of fuel exergy
- Heat transfer to boiler: 15%
- Steam generation irreversibilities: 10%
- Turbine: 5%
- Condenser (low T rejection): 3%
- η_II,plant ≈ 35% (same as η_I only when T_source → ∞; actual η_II > η_I)
Output
Provide: ex_ph [kJ/kg], Ẋ [kW] for streams, Ẋ_destroyed [kW], T₀Ṡ_gen, η_II [%] for each component and overall, identification of highest irreversibility source, minimum energy targets from pinch analysis [kW].
