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The phase transition of a RN-AdS black hole is studied in details usingEhrenfest's equations. There is no discontinuity in entropy which signals alack of any first order phase transition. We then show that althoughEhrenfest's first equation is satisfied, the second is not, so that a truesecond order phase transition is also ruled out. However this deviation fromthe 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 thethermodynamic behaviour using state space geometry and find that the scalarcurvature diverges exactly at those points where the heat capacity diverges.

New type of phase transition in Reissner Nordstr\"om - AdS black hole and its thermodynamic geometry