  In this paper, the thermodynamic property of charged AdS black holes is
studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the
modified dispersion relation, we obtain deformed temperature. Moreover, in
rainbow gravity we calculate the heat capacity in a fixed charge and discuss
the thermal stability. We also obtain a similar behaviour with the liquid-gas
system in extending phase space (including \(P\) and \(r\)) and study its
critical behavior with the pressure given by the cosmological constant and with
a fixed black hole charge \(Q\). Furthermore, we study the Gibbs function and
find its characteristic swallow tail behavior, which indicates the phase
transition. We also find there is a special value about the mass of test
particle which would lead the black hole to zero temperature and a diverging
heat capacity with a fixed charge.
