Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system temperature. This quantity may be difficult to determine or even meaningless unless the system has attained its temperature only through cooling, and not been subjected to work input or output, or any other energy-changing processes.
The internal energy of a system, also often called the thermodynamic energy, includes other forms of energy in a thermodynamic system in addition to thermal energy, namely forms of potential energy that do not influence temperature, such as the chemical energy stored in its molecular structure and electronic configuration, intermolecular interactions associated with phase changes that do not influence temperature (i.e., latent energy), and the nuclear binding energy that binds the sub-atomic particles of matter.
Microscopically, the thermal energy is the kinetic energy of a system's constituent particles, which may be atoms, molecules, electrons, or particles in plasmas. It originates from the individually random, or disordered, motion of particles in a large ensemble. In ideal monatomic gases, thermal energy is entirely kinetic energy. In other substances in cases where some of thermal energy is stored in atomic vibration, this vibrational part of the thermal energy is stored equally partitioned between potential energy of atomic vibration, and kinetic energy of atomic vibration. Thermal energy is thus equally partitioned between all available quadratic degrees of freedom of the particles. As noted, these degrees of freedom may include pure translational motion in gases, in rotational states, and as potential and kinetic energy in normal modes of vibrations in intermolecular or crystal lattice vibrations. In general, due to quantum mechanical reasons, the availability of any such degrees of freedom is a function of the energy in the system, and therefore depends on the temperature (see heat capacity for discussion of this phenomenon).
Macroscopically, the thermal energy of a system at a given temperature is related proportionally to its heat capacity. However, since the heat capacity differs according to whether or not constant volume or constant pressure is specified, or phase changes permitted, the heat capacity cannot be used define thermal energy unless it is done in such a way as to insure that only heat gain or loss (not work) make any changes in the internal energy of the system. Usually, this means constant volume heat capacity so that no work is done, and also the heat capacity of a system for such purposes must not include heat absorbed by any chemical reaction or process.
Thermal energy is not a state function, or a property of a system, since the total thermal energy needed to warm a system to a given temperature depends on the path taken to attain the temperature, unless all forms of work and chemical potential change in the system are zero or negligible. Thus, thermal energy is process-dependent except in systems in which processes to change internal energy other than heating, can be neglected. Nevertheless, when this is true, thermal energy and heat capacity may be a useful concept in the study of heat transfer in solids and liquids, in engineering and other disciplines.
Read more about Thermal Energy: Differentiation From Heat, Definitions, Thermal Energy of The Ideal Gas, Historical Context, Distinction of Thermal Energy and Heat, The Origin of Heat Energy On Earth, Thermal Energy of Individual Particles
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