  For charged black holes in Horava-Lifshitz gravity, a second order phase
transition takes place in extended phase space where the cosmological constant
is taken as thermodynamic pressure. We relate the second order nature of phase
transition to the fact that the phase transition occurs at a sharp temperature
and not over a temperature interval. Once we know the continuity of the first
derivatives of the Gibbs free energy, we show that all the Ehrenfest equations
are readily satisfied. We study the effect of the perturbation of the
cosmological constant as well as the perturbation of the electric charge on
thermodynamic stability of Horava-Lifshitz black hole. We also use
thermodynamic geometry to study phase transition in extended phase space. We
investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and
Quevedo metric in extended phase space of charged Horava-Lifshitz black holes.
It is checked if these curvatures could reproduce the result of specific heat
for the phase transition.
