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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 ...
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 = =.
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.
The equipartition of kinetic energy was proposed initially in 1843, and more correctly in 1845, by John James Waterston. [16] In 1859, James Clerk Maxwell argued that the kinetic heat energy of a gas is equally divided between linear and rotational energy. [17]
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 ...
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.
Rotational energies are quantized. For a diatomic molecule like CO or HCl, or a linear polyatomic molecule like OCS in its ground vibrational state, the allowed rotational energies in the rigid rotor approximation are = = (+) = (+). J is the quantum number for total rotational angular momentum and takes all integer values starting at zero, i.e., =,,, …, = is the rotational constant, and is ...
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...