Boiling water is changing into steam. The specific heat of boiling water is

Specific heat of any substance is the amount of heat transfer $Q$required to cause a unit rise in temperature $∆T$of a unit mass of that substance of mass $m.$

$s=\frac{Q}{m∆T}$

When boiling water changes into steam there is latent heat involved cause its a phase change process, during the phase change process there is no temperature change, therefore, $∆T=0$

Thus, the specific heat of boiling water undergoing through phase change is  $s=\frac{Q}{m∆T}=\frac{Q}{m\times 0}=\infty$