The Boyle temperature is a temperature at which the second virial coefficient vanishes. At that temperature the compressibility factor has no term linear in number density, but higher terms in the virial expansion need not vanish. For a bounded strictly repulsive finite-range pair potential, at every finite positive temperature, with as ; calling its Boyle temperature infinite describes this limiting cancellation, not a finite root.
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Boyle temperature is a concept in thermodynamics that refers to a specific temperature at which a real gas behaves like an ideal gas, regardless of its pressure. This temperature is significant because, for real gases, deviations from ideal gas behavior typically occur at high pressures and low temperatures. At the Boyle temperature, the interactions between gas molecules are minimized, making the gas's behavior more closely resemble that of an ideal gas, which follows Boyle's law (PV = constant) without deviations.