Availability Change⚠ unverified
Physics / Thermodynamics · Compute the flow-availability (exergy) change between two states
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| m | m | kg | 1.0 | Mass of the system |
| u2 | u2 | J/kg | 1.0 | Specific internal energy at state 2 |
| u1 | u1 | J/kg | 1.0 | Specific internal energy at state 1 |
| p2 | p2 | Pa | 1.0 | Pressure at state 2 |
| v2 | v2 | m^3/kg | 1.0 | Specific volume at state 2 |
| p1 | p1 | Pa | 1.0 | Pressure at state 1 |
| v1 | v1 | m^3/kg | 1.0 | Specific volume at state 1 |
| T0 | T0 | K | 1.0 | Absolute dead-state (environment) temperature |
| s2 | s2 | — | 1.0 | Specific entropy at state 2, in joules per kilogram-kelvin (J/(kg.K)) |
| s1 | s1 | — | 1.0 | Specific entropy at state 1, in joules per kilogram-kelvin (J/(kg.K)) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Δψ | J | Change in flow availability (exergy), in joules (J) |
The science & history
Understanding the Parameters
- $u$, $v$, $s$ — thermodynamic properties at the two states (from tables or EOS).
-
$p v$ terms — flow work contribution in the registry’s combined grouping $(u + pv)$ difference, i.e. related to enthalpy $h = u + pv$ when rearranged: $\Delta u + \Delta(pv) = \Delta h$.
-
$T_0$ — environment temperature for the unavailable energy $T_0\Delta s$.
- $s$ — the live calculator labels $s$ as dimensionless; it is J/(kg·K) (or kJ/(kg·K) consistently).
Derivation (Approaching a Proof)
Availability (exergy) is the maximum useful work relative to a dead state $(T_0,p_0,\ldots)$. For a control mass, combining first and second laws with a reversible path to the dead state yields exergy $X = (U-U_0) + p_0(V-V_0) - T_0(S-S_0) + \cdots$. Differences between two states of a flowing stream often use stream availability $\psi = (h-h_0) - T_0(s-s_0) + \frac{V^2}{2} + gz$. The registry implements $m[\Delta u + \Delta(pv) - T_0\Delta s] = m[\Delta h - T_0\Delta s]$, the enthalpy–entropy form without kinetic/potential terms.
History
Availability / exergy analysis (Gouy–Stodola, Keenan, modern second-law design) quantifies lost work beyond first-law efficiency alone.
Related Concepts: Exergy, Exergy Destruction, Availability Efficiency, Entropy Change Ideal Gas, First Law DeltaU
Notes: Registry calculator availability-change (unverified). Unit bug: $s_1$, $s_2$ labelled
dimensionless. No KE/PE; confirm $p v$ units consistent (Pa·m³/kg = J/kg).