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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 significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; this average total kinetic energy is related to the temperature of the system by the equipartition theorem.
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.
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.
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.
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 .
The potential energy is taken to be zero, so that all energy is in the form of kinetic energy. The relationship between kinetic energy and momentum for massive non- relativistic particles is E = p 2 2 m {\displaystyle E={\frac {p^{2}}{2m}}}
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.