  We study the thermodynamics of the 4-dimensional electrically charged
black-hole solutions of the simplest 5-dimensional Kaluza-Klein theory using
Wald's formalism. We show how the electric work term present in the
4-dimensional first law of black-hole thermodynamics arises in the purely
gravitational 5-dimensional framework. In particular, we find an interesting
geometric interpretation of the 4-dimensional electrostatic potential similar
to the angular velocity in rotating black holes. Furthermore, we show how the
momentum map equation arises from demanding compatibility between the timelike
Killing vector of the black-hole solution and the spatial Killing vector of the
5-dimensional background.
