  The phase transition of a RN-AdS black hole is studied in details using
Ehrenfest's equations. There is no discontinuity in entropy which signals a
lack of any first order phase transition. We then show that although
Ehrenfest's first equation is satisfied, the second is not, so that a true
second order phase transition is also ruled out. However this deviation from
the second Ehrenfest's equation, for a certain range of the black hole charge,
indicates the existence of a new glassy type transition. We finally study the
thermodynamic behaviour using state space geometry and find that the scalar
curvature diverges exactly at those points where the heat capacity diverges.
