Thermal Energy - Definitions

Definitions

Thermal energy is the portion of the thermodynamic or internal energy of a system that is responsible for the temperature of the system. The thermal energy of a system scales with its size and is therefore an extensive property. It is not a state function of the system unless the system has been constructed so that all changes in internal energy are due to changes in thermal energy, as a result of heat transfer (not work). Otherwise thermal energy is dependent on the way or method by which the system attained its temperature.

From a macroscopic thermodynamic description, the thermal energy of a system is given by its constant volume specific heat capacity C(T), a temperature coefficient also called thermal capacity, at any given absolute temperature (T):

The heat capacity is a function of temperature itself, and is typically measured and specified for certain standard conditions and a specific amount of substance (molar heat capacity) or mass units (specific heat capacity). At constant volume (V), C_V it is the temperature coefficient of energy. In practice, given a narrow temperature range, for example the operational range of a heat engine, the heat capacity of a system is often constant, and thus thermal energy changes are conveniently measured as temperature fluctuations in the system.

In the microscopical description of statistical physics, the thermal energy is identified with the mechanical kinetic energy of the constituent particles or other forms of kinetic energy associated with quantum-mechanical microstates.

The distinguishing difference between the terms kinetic energy and thermal energy is that thermal energy is the mean energy of disordered, i.e. random, motion of the particles or the oscillations in the system. The conversion of energy of ordered motion to thermal energy results from collisions.

All kinetic energy is partitioned into the degrees of freedom of the system. The average energy of a single particle with f quadratic degrees of freedom in a thermal bath of temperature T is a statistical mean energy given by the equipartition theorem as

where k is the Boltzmann constant. The total thermal energy of a sample of matter or a thermodynamic system is consequently the average sum of the kinetic energies of all particles in the system. Thus, for a system of N particles its thermal energy is

For gaseous systems, the factor f, the number of degrees of freedom, commonly has the value 3 in the case of the monatomic gas, 5 for many diatomic gases, and 7 for larger molecules at ambient temperatures. In general however, it is a function of the temperature of the system as internal modes of motion, vibration, or rotation become available in higher energy regimes.

U_thermal is not the total energy of a system. Physical systems also contains static potential energy (such as chemical energy) that arises from interactions between particles, nuclear energy associated with atomic nuclei of particles, and even the rest mass energy due to the equivalence of energy and mass.