Calculate Brayton cycle efficiency, compressor pressure ratio, or specific heat ratio from any two inputs in an ideal gas turbine cycle.

Brayton Cycle Efficiency Calculator

Enter any 2 values to calculate the missing variable

Brayton Cycle Efficiency Formula

The ideal Brayton cycle thermal efficiency depends on the compressor pressure ratio and the specific heat ratio of the working gas. The calculator uses the air-standard Brayton cycle relation:

= (1 - (1) / (rₚ⁽(k - 1) / k))) * 100

To solve for compressor pressure ratio:

rₚ = ((1) / (1 - / 100))⁽k / (k - 1))

To solve for specific heat ratio:

k = (ln(rₚ)) / (ln(rₚ*(1 - / 100)))
  • η = Brayton cycle thermal efficiency, entered or displayed as a percent
  • rp = compressor pressure ratio, equal to P2 / P1
  • k = specific heat ratio, equal to Cp / Cv
  • ln = natural logarithm

If you leave the efficiency field blank, the calculator uses the first formula to calculate Brayton cycle efficiency. If you leave the pressure ratio blank, it rearranges the efficiency formula to solve for rp. If you leave the specific heat ratio blank, it uses the logarithmic form to solve for k.

These formulas apply to an ideal Brayton cycle with isentropic compression and expansion. Actual gas turbines usually have lower efficiency because of compressor losses, turbine losses, pressure drops, heat losses, and non-ideal combustion.

Typical Specific Heat Ratio Values

The specific heat ratio depends on the gas and temperature. For many Brayton cycle homework calculations using air, k = 1.4 is commonly used.

Gas or Working Fluid Typical k Value Common Use
Air 1.4 Standard Brayton cycle problems
Nitrogen About 1.4 Approximation for air-like behavior
Carbon dioxide About 1.3 Gas calculations where CO2 is the working fluid
Helium About 1.66 Monatomic gas cycle examples

Ideal Brayton Efficiency for Air

The table below shows ideal cycle efficiency values for air using k = 1.4.

Pressure Ratio rp Ideal Efficiency
2 17.97%
5 36.82%
10 48.21%
15 53.86%
20 57.52%

Example Brayton Cycle Efficiency Calculations

Example 1: Find efficiency from pressure ratio and k

Suppose the compressor pressure ratio is 10 and the working fluid is air with k = 1.4.

= (1 - (1) / (10⁽(1.4 - 1) / 1.4))) * 100
= 48.2118\%

The ideal Brayton cycle efficiency is 48.2118%.

Example 2: Find pressure ratio from efficiency and k

Suppose the desired ideal efficiency is 50% and k = 1.4.

rₚ = ((1) / (1 - 50 / 100))⁽1.4 / (1.4 - 1))
rₚ = 11.3137

The required compressor pressure ratio is about 11.3137.

Brayton Cycle Efficiency FAQ

Why does Brayton cycle efficiency increase when pressure ratio increases?

In the ideal Brayton cycle, a higher compressor pressure ratio increases the temperature ratio during isentropic compression and expansion. In the efficiency formula, increasing rp makes the term 1 / rp(k-1)/k smaller, so the efficiency becomes larger.

Why must k be greater than 1?

The specific heat ratio is defined as k = Cp / Cv. For gases used in this type of thermodynamic calculation, Cp is greater than Cv, so k is greater than 1. If k is 1 or less, the ideal Brayton cycle efficiency formula is not valid.

Is this the same as actual gas turbine efficiency?

No. This is the ideal air-standard Brayton cycle efficiency. Actual gas turbine efficiency is affected by compressor efficiency, turbine efficiency, combustor pressure loss, mechanical losses, heat transfer, and real gas behavior. Use this result as an ideal cycle value, not as the guaranteed efficiency of a real machine.