Abstract:
In the absence of work, the exchange of heat of a sample of matter corresponds to the
change of its internal energy, given by the kinetic energy of random translational motion of all its
constituent atoms or molecules relative to the center of mass of the sample, plus the excitation of
quantum states, such as vibration and rotation, and the energy of electrons in excess to their ground
state. If the sample of matter is equilibrated it is described by Boltzmann’s statistical thermodynamics
and characterized by a temperature T. Monotonic motion such as that of the stars of an expanding
universe is work against gravity and represents the exchange of kinetic and potential energy, as
described by the virial theorem, but not an exchange of heat. Heat and work are two distinct
properties of thermodynamic systems. Temperature is defined for the radiative cosmic background
and for individual stars, but for the ensemble of moving stars neither temperature, nor pressure, nor
heat capacities are properly defined, and the application of thermodynamics is, therefore, not advised.
For equilibrated atomic nanoclusters, in contrast, one may talk about negative heat capacities when
kinetic energy is transformed into potential energy of expanding bonds.
