Real-gas behaviour and special temperatures: The temperature at which a real gas most closely obeys Boyle’s law over a range of pressures is called the

Introduction / Context:
Real gases deviate from ideal behavior due to intermolecular forces and finite molecular size. However, at a particular temperature characteristic of each gas, second-order deviations in the pressure–volume relation vanish over a pressure range, and the gas approximately satisfies Boyle’s law (PV ≈ constant). This special temperature is known as the Boyle’s temperature.

Given Data / Assumptions:

• Real gas described by a virial or cubic equation of state.
• At Boyle’s temperature, the second virial coefficient B(T) ≈ 0.
• We compare terminology: triple point, eutectic, inversion temperature, etc.

Concept / Approach:
From the virial expansion, Z = 1 + B(T)P/(RT) + … . If B(T) = 0, then Z ≈ 1 to first order in P, meaning the gas follows Boyle’s law over a finite pressure interval. This temperature, where attractive and repulsive contributions balance such that B(T) vanishes, is the Boyle’s temperature. It is distinct from inversion temperature (related to the sign change in Joule–Thomson coefficient) and from phase-equilibrium points like the triple point or eutectic point.

Step-by-Step Solution:

Verification / Alternative check:
Experimental P–V–T data show near-ideal compressibility at the Boyle’s temperature for many gases (e.g., N2), consistent with B(T_B) ≈ 0.

Why Other Options Are Wrong:

• Triple point/eutectic point: phase-equilibrium points, not gas nonideality minima.
• Inversion temperature: pertains to Joule–Thomson expansion, not Boyle behavior.
• Critical temperature: where gas and liquid become indistinguishable; unrelated to B(T) = 0.

Common Pitfalls:
Confusing Boyle’s temperature with inversion or critical temperatures due to similar-sounding “special” temperatures.

Final Answer:
Boyle’s temperature