Closed-Cycle Gas Turbine – Ideal Compressor Process In an ideal closed-cycle gas turbine (Brayton cycle), the compressor process is modeled as isentropic (adiabatic and reversible).

Difficulty: Easy

Correct Answer: isentropically

Explanation:

Introduction / Context:Cycle modeling requires selecting ideal processes for major components. The Brayton compressor is ideally isentropic, providing a benchmark for defining isentropic efficiency and comparing to real polytropic compression behavior.

Given Data / Assumptions:

  • Closed Brayton loop with compressor, heater, turbine, and cooler.
  • Idealizations: adiabatic, reversible compression and expansion.
  • Working fluid approximated as an ideal gas with nearly constant properties.

Concept / Approach:

An isentropic compressor minimizes required work for a given pressure ratio in the ideal limit. Real compressors are polytropic with efficiencies less than 100%, but the isentropic model is the reference used in performance calculations and definitions (e.g., eta_c = isentropic work / actual work).

Step-by-Step Solution:

Specify desired pressure ratio r_p across the compressor.Model the process as adiabatic and reversible → isentropic.Relate temperature rise using T2/T1 = r_p^{(gamma−1)/gamma} for ideal gas.Use this to compute compressor work and overall cycle efficiency.

Verification / Alternative check:

T-s diagrams show vertical (constant entropy) lines for ideal compression/expansion. Real data deviate rightward due to irreversibilities.

Why Other Options Are Wrong:

Isothermal compression is not Brayton ideal; 'polytropic' describes real behavior but not the ideal assumption; 'none' and 'isobaric' are incorrect for a compressor.

Common Pitfalls:

Using isentropic relations outside their validity (large property variation); confusing stage polytropic efficiency with overall isentropic efficiency.

Final Answer:

isentropically

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