Basic Concept and Simple Examples
See also: Kinetic energy and Heat capacityThe name "equipartition" means "equal division," as derived from the Latin equi from the antecedent, æquus ("equal or even"), and partition from the antecedent, partitionem ("division, portion"). The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. For example, it predicts that every atom of a noble gas, in thermal equilibrium at temperature T, has an average translational kinetic energy of (3/2)kBT, where kB is the Boltzmann constant. As a consequence, since kinetic energy is equal to 1/2(mass)(velocity)2, the heavier atoms of xenon have a lower average speed than do the lighter atoms of helium at the same temperature. Figure 2 shows the Maxwell–Boltzmann distribution for the speeds of the atoms in four noble gases.
In this example, the key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of 1⁄2kBT and therefore contributes 1⁄2kB to the system's heat capacity. This has many applications.
Read more about this topic: Equipartition Theorem
Famous quotes containing the words basic, concept, simple and/or examples:
“The “universal moments” of child rearing are in fact nothing less than a confrontation with the most basic problems of living in society: a facing through one’s children of all the conflicts inherent in human relationships, a clarification of issues that were unresolved in one’s own growing up. The experience of child rearing not only can strengthen one as an individual but also presents the opportunity to shape human relationships of the future.”
—Elaine Heffner (20th century)
“The concept of a person is logically prior to that of an individual consciousness. The concept of a person is not to be analysed as that of an animated body or an embodied anima.”
—Sir Peter Frederick Strawson (b. 1919)
“The real drawback to “the simple life” is that it is not simple. If you are living it, you positively can do nothing else. There is not time.”
—Katharine Fullerton Gerould (1879–1944)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)