Simple Brayton cycle efficiency – dependence on pressure ratio Does the ideal (air-standard) efficiency of a simple gas-turbine cycle depend on the compressor pressure ratio?

Introduction / Context:The simple Brayton (Joule) cycle models gas turbines with two isentropic processes and two constant-pressure processes. A hallmark result is that the air-standard thermal efficiency depends on the pressure ratio across the compressor–turbine pair.

Given Data / Assumptions:

• Air-standard model with constant specific heats.
• Isentropic compression and expansion.
• No intercooling, reheating, or regeneration in the “simple” cycle.

Concept / Approach:The ideal Brayton efficiency may be written as η = 1 − (1 / r_p)^((γ − 1)/γ), where r_p is the pressure ratio and γ = c_p / c_v. This expression shows a direct dependence on r_p: increasing pressure ratio (within limits) increases η, up to an optimum when real effects are considered.

Step-by-Step Solution:Relate temperature ratios to pressure ratio for isentropic stages: T2/T1 = r_p^((γ − 1)/γ).Express heat addition and rejection at constant pressure using temperature differences.Form η = 1 − Q_out/Q_in and simplify to obtain dependence on r_p.Conclude: ideal efficiency increases with r_p per the stated formula.

Verification / Alternative check:Plotting η versus r_p with γ ≈ 1.4 shows monotonic increase for the ideal case, matching standard textbook curves for Brayton cycles without component losses.

Why Other Options Are Wrong:

• “No” contradicts the closed-form efficiency expression.
• Intercooling or regeneration alter efficiency but are not prerequisites for dependence on r_p.
• Non-idealities change the numeric optimum but not the fundamental dependence.

Common Pitfalls:Confusing ideal-cycle results with real-engine optima, which also depend on turbine inlet temperature limits and component efficiencies.

Final Answer:Yes