  This paper is about the extended thermodynamics of AdS black holes and its
relation to CFT thermodynamics. The logarithmic term of the central charge is
interpreted as black hole entropy. We have obtain a modified Friedmann equation
from the Smarr formula. We find that the AdS radius is the critical shadow
radius. We obtain the Hawking-Bekenstein formula with logarithmic corrections,
which depends on the central charge. The real gas in AdS is a dual of an ideal
gas in CFT. This work can be extended to the AdS-Kerr black holes.
