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In 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.
Thus, the ratio of the kinetic energy to the absolute temperature of an ideal monatomic gas can be calculated easily: per mole: 12.47 J/K; per molecule: 20.7 yJ/K = 129 μeV/K; At standard temperature (273.15 K), the kinetic energy can also be obtained: per mole: 3406 J; per molecule: 5.65 zJ = 35.2 meV.
The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.
The kinetic energy of a particular molecule can fluctuate wildly, but the equipartition theorem allows its average energy to be calculated at any temperature. Equipartition also provides a derivation of the ideal gas law , an equation that relates the pressure , volume and temperature of the gas.
Hence, all the energy possessed by the gas is the kinetic energy of the molecules, or atoms, of the gas. E = 3 2 n R T {\displaystyle E={\frac {3}{2}}nRT} This corresponds to the kinetic energy of n moles of a monoatomic gas having 3 degrees of freedom ; x , y , z .
Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.
The average means to average over the kinetic energy of all the particles in a system. If the velocities of a group of electrons , e.g., in a plasma , follow a Maxwell–Boltzmann distribution , then the electron temperature is defined as the temperature of that distribution.
An example is the calculation of the rotational kinetic energy of the Earth. As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of 7.29 × 10 −5 rad·s −1. [2] The Earth has a moment of inertia, I = 8.04 × 10 37 kg·m 2. [3] Therefore, it has a rotational kinetic energy of 2.14 × 10 29 J.