For a gas to be liquefied by pressure, its temperature must be set in what relation to its critical temperature?

Introduction / Context:Gas liquefaction is crucial in cryogenics, storage, and industrial processes (oxygen, nitrogen, LNG). The critical temperature sets a fundamental limit: above it, no amount of pressure alone can condense a gas into a liquid phase.

Given Data / Assumptions:

• Critical temperature T_c is a thermodynamic property of each substance.
• At T > T_c, distinct liquid and vapor phases cannot coexist (supercritical region).

Concept / Approach:To liquefy by compression, the gas must be at T < T_c so that the phase boundary exists. Then increasing pressure moves the state into the two-phase dome, producing liquid. At or above T_c, the fluid becomes supercritical and does not condense into a separate liquid phase with pressure alone.

Step-by-Step Solution:

Verification / Alternative check:CO2 (T_c ≈ 31°C) demonstrates this: at room temperature above T_c, raising pressure produces a supercritical fluid rather than a distinct liquid–vapor mixture.

Why Other Options Are Wrong:

• Above or exactly at T_c: no two-phase region accessible by pressure alone.
• “Unrelated” or “cycled” statements contradict phase-equilibrium fundamentals.

Common Pitfalls:Confusing supercritical fluid density changes with true condensation; visible meniscus and latent heat vanish above T_c.

Final Answer:Lowered below the critical temperature