Brayton Efficiency⚠ unverified
Physics / Thermodynamics · Compute the thermal efficiency of an ideal Brayton cycle
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| rp | rp | — | 1.0 | Pressure ratio across the compressor (dimensionless) |
| gamma | γ | — | 1.4 | Ratio of specific heats (dimensionless). Default is 1.4 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | η | — | Brayton-cycle efficiency (dimensionless) |
The science & history
Understanding the Parameters
-
$r_p$ — higher pressure ratio raises ideal Brayton efficiency (with diminishing returns and material limits on real turbines).
-
$\gamma$ — gas property; affects the exponent $(\gamma-1)/\gamma$.
- $\eta$ — ideal-cycle limit; real engines lower due to compressor/turbine irreversibility and pressure losses.
Derivation (Approaching a Proof)
For isentropic processes on an ideal gas, $T_2/T_1 = r_p^{(\gamma-1)/\gamma} = T_3/T_4$ (standard station numbering). Heat in $q_{\mathrm{in}} = c_p(T_3-T_2)$, heat out $q_{\mathrm{out}} = c_p(T_4-T_1)$, so
$$\eta = 1 - \frac{T_4-T_1}{T_3-T_2} = 1 - \frac{T_1}{T_2} = 1 - r_p^{-(\gamma-1)/\gamma}.$$
History
George Brayton’s engine and later gas turbines use this cycle; jet engines are open Brayton variants.
Related Concepts: Otto Efficiency, Carnot Efficiency, Thermal Efficiency, Rankine Efficiency
Notes: Registry calculator brayton-efficiency (unverified). Ideal air-standard only.