Questions: Isentropic Processes and Reversible Adiabatic Expansion/Compression

Question 1

An engineer analyzing a turbine finds that the actual exit temperature is higher than the temperature predicted by isentropic analysis for the same exit pressure. What does this indicate?

• A. The turbine is extracting more work than the isentropic ideal
• B. The turbine is operating perfectly adiabatically, confirming isentropic behavior
• C. Irreversibilities within the turbine are generating entropy, leaving more thermal energy in the exit stream instead of converting it to shaft work
• D. The turbine has exceeded 100% isentropic efficiency

Answer: (C)

The isentropic exit state represents the minimum possible exit enthalpy for a given inlet state and exit pressure. If the actual exit temperature is higher than isentropic, the exit enthalpy is higher than h₂_isentropic — meaning less enthalpy was extracted as work. The 'missing' work was consumed by irreversibilities (friction, turbulence, flow separation) that generated entropy and left the fluid thermally hotter. Isentropic efficiency η_t = (h₁ − h₂_actual)/(h₁ − h₂_isentropic) < 1.

Question 2

What is the key distinction between an adiabatic process and an isentropic process?

• A. Adiabatic means constant temperature; isentropic means constant entropy
• B. An adiabatic process has no heat transfer but may still generate entropy through irreversibilities; an isentropic process has no heat transfer AND no irreversibilities, so entropy is truly constant
• C. Isentropic processes require small amounts of heat transfer to maintain constant entropy; adiabatic processes do not
• D. There is no difference — all adiabatic processes are isentropic by definition

Answer: (B)

Adiabatic means δQ = 0 — no heat crosses the boundary. But entropy can still be generated inside the system through irreversibilities (friction, viscous dissipation, mixing). From the entropy balance: dS = δQ/T + σ_gen. An adiabatic irreversible process has δQ = 0 but σ_gen > 0, so entropy increases. Only when the process is both adiabatic AND reversible (σ_gen = 0) does entropy remain constant — the isentropic condition. Option D is the most common misconception in this topic.

Question 3

The isentropic efficiency of a real turbine is always less than 100% because irreversibilities leave the exit enthalpy higher than the isentropic ideal, meaning less work was extracted.

• T. True
• F. False

Answer: True

Isentropic efficiency for a turbine is η_t = (h₁ − h₂_actual)/(h₁ − h₂_isentropic). Because real processes always have some irreversibilities, entropy is generated, and the actual exit state has higher enthalpy than the isentropic exit state — less work was extracted. The denominator is always larger than the numerator, giving η_t < 1. Well-designed steam or gas turbines typically achieve 85–92% isentropic efficiency.

Question 4

A process can be simultaneously adiabatic and irreversible while maintaining constant entropy throughout.

• T. True
• F. False

Answer: False

This is thermodynamically impossible. The entropy balance gives dS = δQ/T + σ_gen. An adiabatic process has δQ = 0, so dS = σ_gen. Since irreversibilities generate entropy (σ_gen > 0), an irreversible adiabatic process necessarily increases entropy — it cannot maintain constant entropy. To have dS = 0 with δQ = 0, you need σ_gen = 0, meaning the process must be reversible. Constant entropy requires both conditions simultaneously: no heat transfer and no irreversibilities.

Question 5

Why is the isentropic efficiency formula for a compressor the inverse ratio compared to a turbine — (isentropic work in)/(actual work in) rather than (actual work out)/(isentropic work out)? What would it mean for a compressor to have isentropic efficiency greater than 1?

Model answer: For a turbine, more work output is better, so the efficiency is (actual work)/(isentropic maximum) — the fraction of ideal work actually achieved. For a compressor, less work input is better (achieve the compression with minimum energy), so the efficiency is (isentropic minimum)/(actual work) — the fraction of actual work that would have sufficed under ideal conditions. In both cases, perfect performance gives η = 1 and real performance gives η < 1. A compressor efficiency greater than 1 would mean it requires less work than the isentropic ideal — which would require being reversible and somehow better than reversible, a thermodynamic impossibility.

The definitional choice ensures that isentropic efficiency always falls between 0 and 1 for real devices. This makes efficiencies of different device types directly comparable: η = 0.85 always means 'achieves 85% of theoretical ideal performance,' regardless of whether the device produces or consumes work.