  The equation of state associated with ${\cal N}=4$ supersymmetric Yang-Mills
in 4 dimensions, for $SU(N)$ in the large $N$ limit, is investigated using the
AdS/CFT correspondence. An asymptotically AdS black-hole on the gravity side
provides a thermal background for the Yang-Mills theory on the boundary in
which the cosmological constant is equivalent to a volume. The thermodynamic
variable conjugate to the cosmological constant is a pressure and the $P-V$
diagram is studied. It is known that there is a critical point where the heat
capacity diverges and this is reflected in the isothermal compressibility.
Critical exponents are derived and found to be mean field in the large $N$
limit. The same analysis applied to 3 and 6 dimensional conformal field
theories again yields mean field exponents associated with the compressibility
at the critical point.
