  A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was
considered. Having used the obtained solution we investigated thermodynamic
functions such as black hole's temperature, entropy and heat capacity. In
addition to examine thermodynamic properties of the black hole extended
technique was applied. The equation of state of Van der Waals type was obtained
and investigated. It has been shown that the given system has phase transitions
of the first as well as of the zeroth order for the temperatures below a
critical one which is notable feature of the black hole. A coexistence relation
for two phases was also considered and latent heat was calculated. In the end,
critical exponents were calculated.
