📈 Entropy & Exergy Analysis

Evaluate entropy generation, exergy destruction, and second-law efficiencies for control volumes.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Thermodynamics

📊 Solver Telemetry ● ACTIVE

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⚡ Solves 184

💾 Downloads 387 📦 Fortran Code 11.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

📝 Configuration

Key Equations:

Ṡ_gen = ṁ(s_out − s_in) − Q̇_in/T_source + Q̇_out/T_sink
Ẋ_dest = T₀ · Ṡ_gen (Gouy-Stodola)
ψ = (h − h₀) − T₀(s − s₀)
η_ex = Ẋ_out / Ẋ_in

📊 Results

Configure inputs and click Analyze to view results.

📘 Methodology

Entropy Generation

For any open system at steady state, the entropy balance gives: Ṡ_gen = ṁ(s_out − s_in) − ΣQ̇_k/T_k. Entropy generation is always ≥ 0 (Clausius inequality). It quantifies the total irreversibility in the process.

Exergy & Gouy-Stodola

Exergy (available work) is the maximum useful work obtainable as the system reaches equilibrium with the dead state (T₀, P₀). The Gouy-Stodola theorem states: Ẋ_dest = T₀·Ṡ_gen. This directly links entropy generation to lost work potential.

Dead State & Flow Exergy

The dead state is the environmental reference (typically 25°C, 101.325 kPa). Flow exergy per unit mass: ψ = (h−h₀) − T₀(s−s₀). It combines thermal, mechanical, and chemical exergy components for a flowing stream.

📘 Calculation Methodology: Entropy Generation & Gouy-Stodola Exergy Destruction

Mathematical Model & Theory

Irreversibilities in thermal systems generate entropy $\dot{S}_{gen}$. By the Gouy-Stodola theorem, the lost available work (exergy destruction $\dot{E}_{xd}$) is directly proportional to entropy generation:

$$\dot{S}_{gen} = \frac{d S_{cv}}{dt} - \sum \frac{\dot{Q}_k}{T_k} - \sum \dot{m}_{in} s_{in} + \sum \dot{m}_{out} s_{out} \ge 0$$

$$\dot{E}_{xd} = T_0 \dot{S}_{gen} \quad (\text{Gouy-Stodola Theorem})$$

Assumptions

Second Law of Thermodynamics for open or closed control volume.
Fixed environmental dead-state temperature $T_0$.

Academic References

Bejan, A.: Entropy Generation Minimization, CRC Press.
Moran, M. J.: Availability Analysis: A Guide to Efficient Energy Use.

Worked Engineering Example

Problem Statement:
A heat exchanger transfers $100\text{ kW}$ from a stream at $T_1 = 500\text{ K}$ to a stream at $T_2 = 350\text{ K}$ ($T_0 = 300\text{ K}$). Calculate entropy generation and exergy destruction.

Step-by-step Solution:
1. $\dot{S}_{gen} = \dot{Q}(1/T_2 - 1/T_1) = 100 \times (1/350 - 1/500) = 100 \times (0.002857 - 0.00200) = 0.0857\text{ kW/K}$.
2. $\dot{E}_{xd} = 300\text{ K} \times 0.0857\text{ kW/K} = 25.71\text{ kW}$.
Final Result:
Exergy destruction rate is $\mathbf{25.71\text{ kW}}$ (25.7% of transferred heat).

ThermoFluidCalc Report