Coming back on Thermodynamics, it is possible to consider the situation corresponding to different fundamental statements made from observations of the earlier power engines. An alternative form of the Kelvin-Planck's statement for the Second Law of Thermodynamics is derived, from which parallel results to those of the well established Thermodynamics can be obtained. Special attention is given to the work transfer interactions undergone by Thermodynamic systems experiencing volume-change instead of heat transfer interactions. It is thus possible the construction of a parallel structure for Thermodynamics, here called Pressodynamics, with the volume-change work transfer interactions, the absolute pressure and the volume playing the roles usually played by the heat transfer interactions, the absolute temperature and entropy in the well established Thermodynamics. The irreversibility associated with the volume-change work transfer interactions gives rise to a volume generation, in a parallel way with the entropy generation in the well established Thermodynamics associated with the heat transfer interactions. This volume generation is associated with the lost available mechanical work related with the volume-change work transfer interactions. The obtained results lead to the expansion of the Universe, in a parallel way with the entropy increase of the Universe as given by the well established Thermodynamics. A natural conclusion of the present work is thus the unification of the Thermodynamic and Cosmological time arrows. Some simple application examples are presented. Implications over the usual relations used in Thermodynamics are presented in a companion paper. (c) 2007 Elsevier Ltd. All rights reserved.