Compression path in a closed-cycle gas turbine (theory vs. reality) In a closed Brayton-cycle gas turbine, how is the compression process most accurately described in practice?

Introduction / Context:Thermodynamic textbooks idealize compression as isentropic for efficiency calculations. Real compressors, however, exhibit losses and follow a polytropic path, which more accurately captures the small-step efficiency across many blade rows.

Given Data / Assumptions:

• Closed Brayton cycle using a working gas (e.g., helium, nitrogen, or air in sealed loop).
• Finite mechanical and aerodynamic losses.
• Steady-state operation.

Concept / Approach:Polytropic compression assumes p * v^n = constant with an exponent n between 1 (isothermal) and gamma (isentropic for ideal gas). This provides an incremental efficiency representation and aligns with measured compressor maps.

Step-by-Step Solution:Ideal (reference) path: isentropic.Real path: polytropic with n slightly greater than isothermal and less than isentropic exponent-related equivalent.Therefore, “polytropic” best describes the practical compression process.

Verification / Alternative check:Manufacturers quote polytropic efficiency to characterise multi-row compression more robustly than a single isentropic efficiency figure.

Why Other Options Are Wrong:

• Isothermal: unattainable without ideal heat removal during compression.
• Isentropic: a useful ideal limit, not the real path.
• Isochoric: volume does not remain constant during compression.

Common Pitfalls:Confusing “closed cycle” with “isothermal”; the cycle closure does not imply isothermal compression.

Final Answer:polytropically