**Theoretical Foundation**

Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature. Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy.

The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of classical mechanics, is half the mass of a particle times its speed squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monoatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model.

In the context of thermodynamics, the kinetic energy is also referred to as thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depend on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom.

Read more about this topic: Temperature

### Other articles related to "theoretical foundation, theoretical":

**Theoretical Foundation**

... The structured program theorem provides the theoretical basis of structured programming ... It states that three ways of combining programs—sequencing, selection, and iteration—are sufficient to express any computable function ...

**Theoretical Foundation**

... Ludwig Prandtl at Göttingen was the main center of

**theoretical**and mathematical aerodynamics and fluid dynamics research from soon after 1904 to the end of World War II ...

**Theoretical Foundation**

... Hauer provided a

**theoretical foundation**for the Solomon curve in 1971—“for example, if I drive at 45 mph, while the median of the pack is 60 mph, how ...

### Famous quotes containing the words foundation and/or theoretical:

“The Bermudas are said to have been discovered by a Spanish ship of that name which was wrecked on them.... Yet at the very first planting of them with some sixty persons, in 1612, the first governor, the same year, “built and laid the *foundation* of eight or nine forts.” To be ready, one would say, to entertain the first ship’s company that should be next shipwrecked on to them.”

—Henry David Thoreau (1817–1862)

“Post-structuralism is among other things a kind of *theoretical* hangover from the failed uprising of ‘68Ma way of keeping the revolution warm at the level of language, blending the euphoric libertarianism of that moment with the stoical melancholia of its aftermath.”

—Terry Eagleton (b. 1943)