  We study black-hole thermodynamics in theories that contain dimensionful
constants such as the cosmological constant or coupling constants in Wald's
formalism. The most natural way to deal with these constants is to promote them
to scalar fields introducing a (d-1)-form Lagrange multiplier that forces them
to be constant on-shell. These (d-1)-form potentials provide a dual description
of them and, in the context of superstring/supergravity theories, a
higher-dimensional origin/explanation. In the context of gauged supergravity
theories, all these constants can be collected in the embedding tensor. We show
in an explicit 4-dimensional example that the embedding tensor can also be
understood as a thermodynamical variable that occurs in the Smarr formula in a
duality-invariant fashion. This establishes an interesting link between
black-hole thermodynamics, gaugings and compactifications in the context of
superstring/supergravity theories.
