A gas turbine currently operating at pressure ratio r_p = 20 is redesigned to r_p = 40, with turbine inlet temperature held constant by material limits. The engineer expects higher efficiency. Why might efficiency peak or decline instead?
BThe compressor outlet temperature rises toward the fixed turbine inlet temperature, shrinking the temperature rise the combustor can add and reducing net useful work
CDoubling the pressure ratio always halves the thermal efficiency according to the Brayton formula
DThe working fluid's specific heat ratio γ changes at high pressures, invalidating the efficiency formula
Higher pressure ratio increases the compressor outlet temperature. If turbine inlet temperature is fixed (by blade material limits), the combustor temperature rise ΔT = T_inlet − T_compressor_out shrinks. Less heat is added per unit of compressed air, and the cycle approaches a degenerate limit where the compressor and turbine cancel each other. The efficiency formula η = 1 − 1/r_p^((γ−1)/γ) predicts monotonic improvement only for the ideal cycle with unlimited turbine inlet temperature. In real design, the optimal pressure ratio for maximum efficiency is determined by the turbine inlet temperature limit.
Question 2 Multiple Choice
In the ideal Brayton cycle, the efficiency formula η = 1 − 1/r_p^((γ-1)/γ) is structurally similar to Carnot efficiency 1 − T_cold/T_hot. What does a higher pressure ratio physically accomplish that explains its effect on efficiency?
BHigher r_p increases mass flow through the turbine, producing more shaft work
CHigher r_p expands the exhaust gas further, so turbine exit temperature falls — effectively lowering the 'cold reservoir' temperature and reducing waste heat
DHigher r_p decreases the compressor work, leaving more net output from the turbine
The Brayton efficiency gain from higher pressure ratio comes from more complete expansion in the turbine. With higher r_p, the turbine expands the gas over a larger pressure range, extracting more work and exhausting at a lower temperature. This is analogous to reducing T_cold in the Carnot formula — less heat is rejected to the atmosphere. The key physical insight is that it is the turbine exit temperature, not the combustor temperature, that determines how much energy is wasted.
Question 3 True / False
In a combined-cycle power plant, the hot gas turbine exhaust (at ~550°C) is used to generate steam for a Rankine bottoming cycle, raising overall plant efficiency well above what the simple Brayton cycle alone achieves.
TTrue
FFalse
Answer: True
A simple-cycle gas turbine exhausts at 500–600°C — still very hot, representing a large fraction of unrecovered thermal energy. A heat recovery steam generator (HRSG) captures this waste heat to produce steam, driving a second (Rankine) turbine. The combined system achieves 55–60% thermal efficiency versus 35–40% for the gas turbine alone. The efficiency gain is not from burning more fuel but from extracting useful work from heat that would otherwise be vented to the atmosphere. This is why virtually all modern natural-gas power plants are combined-cycle.
Question 4 True / False
In real gas turbine operation, increasing the compressor pressure ratio usually improves thermal efficiency regardless of the turbine inlet temperature constraint.
TTrue
FFalse
Answer: False
Real turbine blades have material temperature limits (~1400–1600°C for modern superalloys with cooling). As pressure ratio increases, compressor outlet temperature rises. If turbine inlet temperature is fixed, the temperature difference across the combustor shrinks, reducing the heat addition per unit mass flow. At some pressure ratio, this effect dominates, and efficiency peaks then declines. Even for the ideal Brayton cycle, real engineering optimization always involves the turbine inlet temperature as a co-parameter — the optimal pressure ratio increases with turbine inlet temperature, making materials research and blade cooling as important as compressor design.
Question 5 Short Answer
Explain why combining a gas turbine with a steam turbine (combined cycle) approaches 60% efficiency while the gas turbine alone achieves only 35–40%.
Think about your answer, then reveal below.
Model answer: The gas turbine exhausts at 500–600°C — still containing substantial thermal energy that a simple-cycle plant vents to the atmosphere. In a combined-cycle plant, this exhaust passes through a heat recovery steam generator that produces steam for a Rankine bottoming cycle. The Rankine cycle converts a significant fraction of that waste heat into additional shaft work. Because no additional fuel is burned, the extra electricity comes 'free' from heat that was already in the system. The combined first-law efficiency reflects the sum of both cycles' work outputs divided by the original fuel input.
The thermodynamic principle is that the combined cycle attacks waste heat from both ends: the Brayton cycle does not exhaust until temperatures drop to ~550°C, and the Rankine cycle starts with that 550°C steam. Each Joule that would have been rejected by the simple Brayton cycle is now a potential input to the bottoming cycle. The practical limit is set by Rankine cycle efficiency at its operating temperatures (~30–35%) and by HRSG heat transfer effectiveness. The result — 55–60% — is close to the theoretical maximum for a two-stage cascade operating between combustion temperature and ambient.