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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, $B_2(T)>0$ at every finite positive temperature, with $B_2(T)\to 0$ as $T\to \infty$; calling its Boyle temperature infinite describes this limiting cancellation, not a finite root.

The compressibility factor is the ratio $p/(n{k}_{B}T)$, where $n$ is number density. A classical ideal gas has $Z=1$. The virial expansion writes $Z=1+B_{2}n+B_3{n}^2+\cdots$ for a dilute gas; this dimensionless ratio is distinct from isothermal compressibility, which is a response derivative with units of inverse pressure.