  We develop an analogy between fluids and black holes to study phase
transitions in the latter. The entropy-temperature graph shows the onset of a
phase transition without any latent heat. The nature of this continuous (higher
order) phase transition is examined in details. We find that the second order
derivatives of the free energy diverge at the critical temperature. Also, the
transition is smeared instead of sharp, so that the usual Ehrenfest's scheme
breaks down. A generalised version of this scheme is formulated which is shown
to be consistent with the phase transition curves.
