  In this paper, we analyze the complete thermodynamic and phase transition
phenomena of a black hole solution in Ho\v{r}ava-Lifshitz gravity in arbitrary
space time. Nature of phase transition is studied using geometrothermodynamic
and Ehrenfest's scheme of standard thermodynamics. We analytically check the
Ehrenfest's equations near the critical point, which is the point of divergence
in the heat capacity. Our analysis revels that this black hole exhibits a
second order phase transition.
