  Moir\'e superlattices of transitional metal dichalcogenides exhibit strong
electron-electron interaction that has led to experimental observations of Mott
insulators and generalized Wigner crystals. In this letter, we report direct
measurements of the thermodynamic gaps of these correlated insulating states in
a dual-gate WS2/WSe2 moir\'e bilayer. We employ the microwave impedance
microscopy to probe the electronic features in both the graphene top gate and
the moir\'e bilayer, from which we extract the doping dependence of the
chemical potential of the moir\'e bilayer and the energy gaps for various
correlated insulating states utilizing the Landau quantization of graphene.
These gaps are relatively insensitive to the application of an external
electric field to the WS2/WSe2 moir\'e bilayer.
