Engineering
Ideal constant-specific-heat Brayton efficiency and compressor temperature
Explore the ideal Brayton pressure-ratio expression and isentropic compression temperature, with explicit thermodynamic assumptions.
Use an ideal cycle, not a measured engine efficiency
This cold-air-standard model assumes a calorically perfect gas with constant gamma, isentropic compression and expansion, constant-pressure heat addition and rejection, no pressure losses and no regeneration. It is not the propulsive or overall efficiency of an aircraft engine.
A higher pressure ratio increases this ideal expression, but it also raises compressor temperature. A real cycle needs adequate turbine inlet temperature and positive net work; this worksheet has no turbine temperature or component losses and cannot optimize an engine. Gamma=1.4 is an illustrative constant, not a universal high-temperature air property.
Use absolute pressures for the ratio and kelvin for inlet temperature. Require pressure ratio at least1, gamma greater than1 and positive absolute temperature. At ratio1, the expression returns its zero-efficiency limit; this is a degenerate cycle, not a functioning power plant.
| Brayton Turbine Metric | Formula | Illustrative ratio16, T1=288.15 K | Illustrative ratio40, same inlet |
|---|---|---|---|
| Isentropic Temp Ratio T2 / T1 | B2 ^ ((B3 - 1) / B3) | 16 ^ (0.4/1.4) = 2.2082 | 40 ^ (0.4/1.4) = 2.8690 |
| Ideal Brayton Efficiency eta | 1 - (1 / (B2 ^ ((B3 - 1) / B3))) | 54.71% (0.5471) | 65.14% (0.6514) |
| Compressor Exit Temp T2 (K) | B4 * (B2 ^ ((B3 - 1) / B3)) | 636.29 K (363.1 °C) | 826.70 K (553.6 °C) |
Ideal Brayton Cycle Thermal Efficiency = 1 - (1 / r_p^((gamma - 1) / gamma))
Evaluates isentropic pressure-ratio efficiency from r_p (B2) and specific heat ratio gamma (B3).
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<1,B3<=1,B4<=0),"Invalid inputs",ROUND(1 - (1 / (B2 ^ ((B3 - 1) / B3))), 4)))Isentropic Compressor Discharge Temperature T2 (Kelvin)
Multiplies absolute Kelvin inlet temperature B4 by isentropic temperature ratio.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<1,B3<=1,B4<=0),"Invalid inputs",ROUND(B4 * (B2 ^ ((B3 - 1) / B3)), 2)))Try the example
Use the original values or change them to test your understanding.