Exergy⚠ unverified
Physics / Thermodynamics · Compute the exergy (availability) of a heat transfer
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 temperature of the dead-state (environment) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | X | J | Exergy of the heat, in joules (J). Returns 0.0 if ``T`` is not positive |
The science & history
Understanding the Parameters
- $Q$ — quantity of heat (not power); same energy units as $X$.
- $T$ — hotter source → larger fraction $(1-T_0/T)$ available as work.
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$T_0$ — colder environment → more of $Q$ is available; require $T > T_0 > 0$ for positive $X$ from a heat source above ambient.
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$X$ — equals $Q\,\eta_{\mathrm{Carnot}}$ for reservoirs $T$ and $T_0$.
Derivation (Approaching a Proof)
A Carnot engine taking $Q$ from $T$ and rejecting to $T_0$ has $\eta = 1 - T_0/T$, so maximum work is
$$W_{\max} = Q\left(1 - \frac{T_0}{T}\right) = X.$$
Unavailable energy is $Q\,T_0/T$, dumped as heat to the environment in the reversible limit.
History
Exergy / availability formalises “quality of energy”; heat at higher $T$ is more valuable than the same joules near ambient — central to second-law design.
Related Concepts: Carnot Efficiency, Exergy Destruction, Availability Change, Availability Efficiency
Notes: Registry calculator exergy (unverified). Heat-exergy form only (not flow stream exergy).