Rankine Efficiency⚠ unverified
Physics / Thermodynamics · Compute the thermal efficiency of a Rankine cycle
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| turbine_work | turbinework | J | 1.0 | Work output of the turbine |
| pump_work | pumpwork | J | 1.0 | Work input to the pump |
| heat_added | heatadded | J | 1.0 | Heat added |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | η | — | Rankine-cycle efficiency (dimensionless). Returns 0.0 if ``heat_added`` is not positive |
The science & history
Understanding the Parameters
- $W_t$ — usually $h_3 - h_4$ (specific) times mass; keep the same basis as $W_p$ and $Q_{\mathrm{in}}$.
- $W_p$ — often small vs $W_t$ but required for net work; $W_{\mathrm{net}} = W_t - W_p$.
- $Q_{\mathrm{in}}$ — heat to the working fluid in the steam generator.
- $\eta$ — real plants ~30–45% depending on superheat, reheat, regeneration; still below Carnot between the same extreme temperatures.
Derivation (Approaching a Proof)
For a cycle, $\eta = W_{\mathrm{net}}/Q_{\mathrm{in}}$ by definition. In the Rankine layout, $W_{\mathrm{net}} = W_{\mathrm{turbine}} - W_{\mathrm{pump}}$, hence
$$\eta = \frac{W_t - W_p}{Q_{\mathrm{in}}}.$$
Ideal Rankine analyses compute each term from steam-table enthalpies at the four (or more) states.
History
The Rankine cycle models steam engines and modern steam power plants; it remains the thermodynamic backbone of thermal electricity generation.
Related Concepts: Thermal Efficiency, Carnot Efficiency, Brayton Efficiency, Otto Efficiency, First Law DeltaU
Notes: Registry calculator rankine-efficiency (unverified). Definitional net-work form; does not
look up steam properties.