A gas turbine produces 900 kJ/kg of gross turbine work and has a back work ratio of 45%. What is the net work output?
A900 kJ/kg — the back work ratio in gas turbines is negligible
B495 kJ/kg
C810 kJ/kg — only friction losses reduce the gross output
D450 kJ/kg
Back work ratio = compressor work / turbine work = 0.45, so compressor work = 0.45 × 900 = 405 kJ/kg. Net work = 900 − 405 = 495 kJ/kg. Option A is the classic misconception from confusing the Brayton cycle with the Rankine cycle, where the pump consumes only 1–2% of turbine output. In the Brayton cycle, compressing a gas (rather than a nearly incompressible liquid) requires enormous work, making the back work ratio one of the cycle's defining characteristics.
Question 2 Multiple Choice
A Rankine cycle pump and a Brayton cycle compressor each raise the working fluid from 1 bar to 100 bar. The pump consumes about 10 kJ/kg while the compressor consumes about 450 kJ/kg. What is the fundamental reason for this 45-fold difference?
AThe Brayton compressor is less aerodynamically efficient than the Rankine pump
BThe Rankine cycle operates at lower pressure ratios in practice, reducing pump work
CCompressing a gas requires far more work than compressing a nearly incompressible liquid to the same pressure, because a gas has much larger specific volume throughout compression
DThe Brayton cycle uses air as the working fluid, which has a higher molecular weight than steam
The work required to compress a fluid equals the integral of v dP along the compression path. For liquid water, specific volume v is tiny and nearly constant, making pump work ≈ v(P₂ − P₁) — very small. For air (a gas), specific volume is orders of magnitude larger throughout compression, making the integral far larger. This is a fundamental thermodynamic consequence of the state of the working fluid, not an engineering imperfection. It is precisely why Rankine cycles condense steam to liquid before pumping — doing so dramatically reduces compression work.
Question 3 True / False
In the ideal Brayton cycle, increasing the pressure ratio always increases the thermal efficiency.
TTrue
FFalse
Answer: True
The ideal Brayton efficiency is η = 1 − (P₁/P₂)^((γ−1)/γ) = 1 − 1/r_p^((γ−1)/γ). Since the exponent (γ−1)/γ is positive (≈ 0.286 for air with γ ≈ 1.4), r_p^((γ−1)/γ) increases monotonically with pressure ratio, so the subtracted term decreases and η increases. Real engines have a practical optimum because compressor irreversibilities grow at high pressure ratios and turbine inlet temperature is materials-limited — but these are departures from the ideal, not contradictions of it.
Question 4 True / False
In a real Brayton cycle, turbine irreversibilities are more damaging to net work output than compressor irreversibilities of the same fractional magnitude, because the turbine produces most of the useful work.
TTrue
FFalse
Answer: False
Compressor irreversibilities are typically more damaging in practice, precisely because of the large back work ratio. A 10% increase in compressor work (due to irreversibility) on a baseline of 400 kJ/kg cuts net work by 40 kJ/kg. Additionally, compressor fouling from airborne particles is a common real-world degradation mechanism. The claim that turbine irreversibilities are worse confuses gross output with net output — the compressor's large fraction of turbine work means the multiplied effect of compressor inefficiency is severe, and it is often the tighter design constraint.
Question 5 Short Answer
Explain why the back work ratio in the Brayton cycle is so much larger than in the Rankine cycle, and what consequence this has for how sensitive gas turbine net output is to compressor isentropic efficiency.
Think about your answer, then reveal below.
Model answer: In the Brayton cycle the working fluid is always a gas, and compressing a gas requires work proportional to its specific volume integrated over the pressure rise — far more than compressing a liquid to the same pressure. The Rankine cycle avoids this by condensing steam to liquid before pumping, making pump work negligible. Because the Brayton compressor consumes 40–50% of gross turbine output, a small drop in compressor isentropic efficiency has a large absolute effect on net work: if the compressor needs 10% more work due to internal losses, that 10% is applied to the already-large compressor baseline, cutting net output by a disproportionate fraction.
This explains why gas turbine designers invest heavily in compressor aerodynamics and why compressor fouling — from airborne particles coating blade surfaces — is a major maintenance concern in industrial and aviation gas turbines. A few percent reduction in compressor efficiency can meaningfully reduce power output and increase specific fuel consumption.