What Is Heat? Can Heat Capacities Be Negative?

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.

Automated summary

In the absence of work, heat exchange in a sample corresponds to the change in internal energy, which includes kinetic energy of atoms/molecules, excitation of quantum states, and excess electron energy. Equilibrated samples can be described by Boltzmann's statistical thermodynamics and characterized by temperature T. Monotonic motion of stars in an expanding universe involves work against gravity and the exchange of kinetic and potential energy, but not heat. Heat and work are distinct properties in thermodynamic systems. For moving stars, temperature, pressure, and heat capacities are not properly defined, so applying thermodynamics is not advised. However, equilibrated atomic nanoclusters can exhibit negative heat capacities when kinetic energy is transformed into potential energy of expanding bonds.