Air-cycle refrigeration (Bell–Coleman) — typical applications Identify where the air refrigeration (reverse Brayton) cycle is commonly employed in practice.

Introduction / Context:
The air (Bell–Coleman) refrigeration cycle uses air as the working fluid and relies on compression, heat rejection, expansion, and heat absorption. Unlike vapor-compression systems, it has no phase change and typically lower coefficient of performance, but it offers simplicity and direct use of available air streams.

Given Data / Assumptions:

• A standard air-cycle (reverse Brayton) system with compressors and expansion turbines.
• Focus on mainstream, widely accepted applications.
• Comparison with common vapor-compression uses.

Concept / Approach:
Air-cycle systems are favored where weight, simplicity, and abundant cooling air are available—most notably in aircraft environmental control systems. The lower COP is acceptable because engine bleed air and high-speed ram air can be utilized, and environmental control packs are compact and reliable. For domestic or commercial refrigeration, vapor-compression systems dominate due to higher efficiency and more convenient components.

Step-by-Step Solution:
List typical domains: aircraft cabin air-conditioning; some transport or military applications.Evaluate options: domestic and commercial refrigerators overwhelmingly use vapor-compression with refrigerants like R-134a or R-600a.Gas liquefaction employs specialized cycles (Claude, Linde) not the simple Bell–Coleman air cycle for general service.Therefore, the correct broad category is air-conditioning (especially aircraft).

Verification / Alternative check:
Aircraft environmental control systems (ECS) are textbook examples of air-cycle refrigeration, confirming “air-conditioning” as the appropriate choice.

Why Other Options Are Wrong:
(a) and (b) use vapor-compression for efficiency and practicality. (d) Gas liquefaction cycles are different and optimized for cryogenic temperatures. (e) Ice plants also prefer vapor-compression due to better COP.

Common Pitfalls:
Assuming “refrigeration” always means household fridges; different thermodynamic needs lead to different cycles in aerospace versus domestic contexts.

Final Answer:
air-conditioning