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A polyatomic gas, like water, is not radially symmetric about any axis, resulting in D = 6, comprising 3 translational and 3 rotational degrees of freedom. Because the equipartition theorem requires that kinetic energy is partitioned equally, the total kinetic energy is = =.
Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation , the following dependence on the object's moment of inertia is observed: [ 1 ] E rotational = 1 2 I ω 2 {\displaystyle E_{\text ...
The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Thomas Young, who in his 1802 lecture to the Royal Society, was the first to use the term energy to refer to kinetic energy in its modern sense, instead of vis viva.
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [1] [2] [3] Albert Einstein in 1905, [4] and by Marian Smoluchowski in 1906 [5] in their works on Brownian motion.
For example, if the particles are rigid mass dipoles of fixed dipole moment, they will have three translational degrees of freedom and two additional rotational degrees of freedom. The energy in each degree of freedom will be described according to the above chi-squared distribution with one degree of freedom, and the total energy will be ...
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1.The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
By the equipartition theorem, internal energy per mole of gas equals c v T, where T is absolute temperature and the specific heat at constant volume is c v = (f)(R/2). R = 8.314 J/(K mol) is the universal gas constant, and "f" is the number of thermodynamic (quadratic) degrees of freedom, counting the number of ways in which energy can occur.