Equipartition Theorem - Basic Concept and Simple Examples

Basic Concept and Simple Examples

See also: Kinetic energy and Heat capacity

The 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:

    “It is not an exaggeration to say that play is as basic to your child’s total development as good food, cleanliness, and rest.”
    —Joanne E. Oppenheim (20th century)

    “The new concept of the child as equal and the new integration of children into adult life has helped bring about a gradual but certain erosion of these boundaries that once separated the world of children from the word of adults, boundaries that allowed adults to treat children differently than they treated other adults because they understood that children are different.”
    —Marie Winn (20th century)

    “We black men seem the sole oasis of simple faith and reverence in a dusty desert of dollars and smartness.”
    —W.E.B. (William Edward Burghardt)

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)