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In this work the \textit{chemistry} of asymptotically AdS black hole, chargedand uncharged, solutions of Pure Lovelock gravity is discussed. For this themass parameter of black holes is identified with the enthalpy of the systemtogether with the promotion of the cosmological constant to a thermodynamicsvariable proportional to the \textit{pressure} of the system. The equations ofstate for both, charged and uncharged, are obtained. It is shown that thecharged case behaves as a Van der Waals fluid. The existence of a first orderphase transition between small stable/large stable black hole, which is areminiscent of the liquid/gas transition, is found. The critical exponents ofthe thermal evolution, for different cases of interest, are similar to those ofthe Van der Waals fluid.

Thermodynamic extended phase space and $P-V$ criticality of black holes at Pure Lovelock gravity