Real-gas behaviour:\nThe temperature at which the second virial coefficient (B) of a real gas becomes zero is known as the ________.

Introduction / Context:
The virial equation of state expands real-gas behaviour in powers of 1/V or p, with the second virial coefficient B(T) capturing pairwise interactions. The temperature where B(T) = 0 is important because the gas shows nearly ideal compressibility over a moderate pressure range.

Given Data / Assumptions:

• Definition of B(T) as a function of temperature alone for a given gas.
• Classical virial EoS context.

Concept / Approach:
At the Boyle temperature, Z = pV/RT approaches 1 with minimal slope at low pressures, since the first correction term (involving B) vanishes. This does not mean perfect ideality at all pressures; higher virial terms still matter at higher p.

Step-by-Step Solution:
Recall virial form: Z = 1 + B(T)p/RT + C(T)p^2/…Set B(T) = 0 → lowest-order deviation disappears.By definition, this T is the Boyle temperature.

Verification / Alternative check:
Compressibility-factor charts show that near the Boyle temperature, the Z–p curve is flat at low p.

Why Other Options Are Wrong:
Eutectic relates to solid–solid–liquid equilibria; boiling and critical temperatures are phase-change properties; consolute point applies to liquid–liquid miscibility.

Common Pitfalls:
Confusing Boyle temperature with Boyle’s law (isothermal ideality) at any temperature—real gases approximate it only near this special temperature at low p.

Final Answer:
Boyle temperature