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Kinetic theory of gases. The temperature of the ideal gas is proportional to the average kinetic energy of its particles. The size of helium atoms relative to their spacing is shown to scale under 1,950 atmospheres of pressure. The atoms have an average speed relative to their size slowed down here two trillion fold from that at room temperature.
Since the kinetic energy is quadratic in the components of the velocity, by equipartition these three components each contribute 1 ⁄ 2 k B T to the average kinetic energy in thermal equilibrium. Thus the average kinetic energy of the particle is 3 / 2 k B T, as in the example of noble gases above.
In other words, its potential energy is zero. Hence, all the energy possessed by the gas is the kinetic energy of the molecules, or atoms, of the gas. = This corresponds to the kinetic energy of n moles of a monoatomic gas having 3 degrees of freedom; x, y, z. The table here below gives this relationship for different amounts of a monoatomic gas.
The kinetic energy is equal to 1/2 the product of the mass and the square of the speed. In formula form: where is the mass and is the speed (magnitude of the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.
m = mass of each molecule (all molecules are identical in kinetic theory), γ (p) = Lorentz factor as function of momentum (see below) Ratio of thermal to rest mass-energy of each molecule: θ = k B T / m c 2 {\displaystyle \theta =k_ {\text {B}}T/mc^ {2}} K2 is the modified Bessel function of the second kind.
In statistical mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path) with that of the total potential energy of the system. Mathematically, the theorem states ...
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics , which deals with the direction in which a reaction occurs but in itself tells nothing about its rate.
An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi–Dirac statistics. The equivalent model for integer spin particles is called the Bose gas (an ensemble of non ...