In thermodynamics of real gases, the temperature at which a real gas most closely obeys the ideal gas law across a wide range of pressure is called the Boyle temperature. What is this term known as?

Introduction / Context:
The ideal gas law PV = nRT is an approximation that becomes exact only when intermolecular forces are negligible. Real gases deviate from ideality due to attractions and repulsions. There exists a special temperature at which the first departures from ideality cancel out over a range of pressures, giving behavior that closely tracks the ideal gas law. This temperature is known as the Boyle temperature and is a standard concept in physical chemistry and chemical engineering thermodynamics.

Given Data / Assumptions:

• Single-component real gas considered.
• Behavior evaluated over a moderate pressure range near low pressure.
• Use of virial equation to quantify deviation from ideality.

Concept / Approach:
Real-gas behavior can be represented by the virial equation of state: Z = PV/(nRT) = 1 + B(T)P/RT + C(T)(P/RT)^2 + … . The second virial coefficient B(T) captures the dominant effects of intermolecular forces at low to moderate pressures. The Boyle temperature TB is defined by B(TB) = 0. At T = TB, the compressibility factor Z ≈ 1 over a finite pressure range because the first correction term vanishes, causing the gas to mimic ideal behavior better than at other temperatures.

Step-by-Step Solution:

Verification / Alternative check:
From pair potential models (e.g., Lennard-Jones), B(T) changes sign with T; a specific T exists where attractions and repulsions balance so that the second virial term vanishes. Experimental compressibility plots Z vs. P at TB pass nearly through Z = 1 with minimal slope, confirming the definition.

Why Other Options Are Wrong:

• Reduced: refers to dimensionless variables (Pr, Tr).
• Critical: associated with phase transition at Pc, Tc.
• Inversion: relates to Joule–Thomson coefficient changing sign.
• Pseudo-critical: used for gas mixtures, not this concept.

Common Pitfalls:
Confusing Boyle temperature with inversion temperature; the former concerns virial behavior near low pressure, the latter concerns throttling temperature effects.

Final Answer:
Boyle