Exergy Destruction⚠ unverified
Physics / Thermodynamics · Compute the exergy destruction due to irreversibility
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Q | Q | J | 1.0 | Heat transferred |
| T | T | K | 1.0 | Absolute temperature of the heat source |
| T0 | T0 | K | 1.0 | Absolute dead-state (environment) temperature |
| S_gen | Sgen | J/K | 1.0 | Entropy generated by the irreversibility |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Xdestroyed | J | Exergy destruction, in joules (J) |
The science & history
Understanding the Parameters
-
$S_{\mathrm{gen}}$ — from entropy balance: $S_{\mathrm{gen}} = \Delta S_{\mathrm{sys}} - \sum Q_j/T_j$ (closed system form); always $\ge 0$ (second law).
-
$T_0$ — converts entropy generation into lost work units (joules).
- $Q$, $T$ — might have been intended for $S_{\mathrm{gen}} = Q/T$ style estimates but are ignored by $X = T_0 S_{\mathrm{gen}}$. Use Second Law Entropy separately if needed.
Derivation (Approaching a Proof)
Combining first and second laws for a process interacting with an environment at $T_0$, the gap between reversible work and actual work equals $T_0 S_{\mathrm{gen}}$ (Gouy–Stodola theorem). Hence exergy destruction is defined as
$$X_{\mathrm{dest}} = T_0 S_{\mathrm{gen}}.$$
History
Gouy (1889) and Stodola linked entropy production to lost work; it is the quantitative backbone of exergy analysis.
Related Concepts: Exergy, Second Law Entropy, Availability Efficiency, Availability Change
Notes: Registry calculator exergy-destruction (unverified). Unused inputs: $Q$, $T$.
Formula is only $T_0 S_{\mathrm{gen}}$.