Thermal Efficiency⚠ unverified
Physics / Thermodynamics · Thermal efficiency of a heat engine
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| W_net | W | J | 300.0 | Net work output |
| Q_in | Qin | J | 1000.0 | Heat input |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| efficiency | η | — | Thermal efficiency |
The science & history
Understanding the Parameters
-
$W_{\mathrm{net}}$ — turbine work minus pump work, or indicated work, depending on the boundary; must be the work you count as “output.”
-
$Q_{\mathrm{in}}$ — heat added (fuel energy, boiler heat, …), not total energy throughput.
- $\eta$ — e.g. $W=300\,\text{J}$, $Q_{\mathrm{in}}=1000\,\text{J}$ → $\eta = 0.3$. Always $\eta \le \eta_{\mathrm{Carnot}}$ for the same $T_h$, $T_c$.
Derivation (Approaching a Proof)
For a cyclic engine, $\Delta U = 0$ over a cycle, so $W_{\mathrm{net}} = Q_{\mathrm{net}} = Q_{\mathrm{in}} - |Q_{\mathrm{out}}|$ (first law). Efficiency is defined as useful work per heat purchased:
$$\eta \equiv \frac{W_{\mathrm{net}}}{Q_{\mathrm{in}}}.$$
No second-law content until you compare to Carnot Efficiency.
History
Thermal efficiency is the primary figure of merit for heat engines since the industrial revolution; modern combined-cycle plants chase high $\eta$ against the Carnot ceiling.
Related Concepts: Carnot Efficiency, Rankine Efficiency, Otto Efficiency, Brayton Efficiency, First Law DeltaU
Notes: Registry calculator thermal-efficiency (unverified). Definitional; consistent energy
units required.