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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.
In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
Robot arms are described by their degrees of freedom. This is a practical metric, in contrast to the abstract definition of degrees of freedom which measures the aggregate positioning capability of a system. [3] In 2007, Dean Kamen, inventor of the Segway, unveiled a prototype robotic arm [4] with 14 degrees of freedom for DARPA.
A typical phase diagram.The solid green line applies to most substances; the dashed green line gives the anomalous behavior of water. In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. [1]
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.
Solid: A solid holds a definite shape and volume without the need of a container. The particles are held very close to each other. Amorphous solid: A solid in which there is no far-range order of the positions of the atoms. Crystalline solid: A solid in which atoms, molecules, or ions are packed in regular order.
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It therefore has f = 3 + 3 + 2(3n − 6) = 6n − 6 energy-absorbing degrees of freedom (one less than a linear molecule with the same atom count). Water H 2 O (n = 3) is bent in its non-strained state, therefore it is predicted to have f = 12 degrees of freedom. [19] Methane CH 4 (n = 5) is tridimensional, and the formula predicts f = 24.