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Definition Of Thermal Energy.
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 and it is a state function of the system. It is independent of the way or method by which the system attained this energy.
From a macroscopic thermodynamic description, the thermal energy of a system is given by its 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), CV it is the temperature coefficient of energy, while at constant pressure (p), Cp is the coefficient of enthalpy. aIn 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 static 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 Blotzmann 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.
Uthermal 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.
Explanation.
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system temprature. The internal energy, also often called the thermodynamic energy, includes other forms of energy in a thermodynamic system ina 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 partly 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 subtances 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 partioned 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 phenomena).
Macroscopically, the thermal energy of a system at a given temperature is related proportionally to its heat capacity.
Thermal energy is distinct from heat. Thermal energy is a state function, a property of a system, while heat, in the strict use in physics, is characteristic only of a process, i.e. it is absorbed or produced as an energy exchange, always as a result of a temperature difference. It is not a static property of matter. Matter does not contain heat, but rather thermal energy. Heat is thermal energy in the process of transfer or conversion across a boundary of one region of matter to another, as a result of a temperature difference. In engineering, the terms "heat" and "heat transfer" are thus used interchangably, since heat is always understood to be in the the process of transfer. The energy transfered by heat is called by other terms (such as thermal energy or latent energy) when this energy is no longer in net transfer, and has become static.
When two thermodynamic systems with different temperatures are brought into diathermic contact, they spontaneously exchange energy as heat, which is a transfer of thermal energy from the system of higher temperature to the colder system. Heat may cause work to be performed on a system, for example, in form of volume or pressure changes. This work may be used in heat engines to convert thermal energy into other forms of energy. In geothermal power plants it is used for the generation of electricity. When two systems have reached a thermodynamic equilibrium, they have attained the same temperature and the net exchange of thermal energy vanishes--heat ceases.
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