The Lennard–Jones model predicts a more complicated T T -dependence, but is more accurate than the other three models and is widely used in engineering practice. The predictions of the first three models (hard-sphere, power-law, and Sutherland) can be simply expressed in terms of elementary functions. The viscosity predictions for four molecular models are discussed below. In particular, given a model for intermolecular interactions, one can calculate with high precision the viscosity of monatomic and other simple gases (for more complex gases, such as those composed of polar molecules, additional assumptions must be introduced which reduce the accuracy of the theory). The theoretical basis of the kinetic theory is given by the Boltzmann equation and Chapman–Enskog theory, which allow accurate statistical modeling of molecular trajectories. The kinetic theory of gases allows accurate calculation of the temperature-variation of gaseous viscosity. See also: Kinetic theory of gases and Chapman–Enskog theory An everyday example of this viscosity decrease is cooking oil moving more fluidly in a hot frying pan than in a cold one. Increasing temperature results in a decrease in viscosity because a larger temperature means particles have greater thermal energy and are more easily able to overcome the attractive forces binding them together. In liquids, viscous forces are caused by molecules exerting attractive forces on each other across layers of flow. Hence, gaseous viscosity increases with temperature. Since the momentum transfer is caused by free motion of gas molecules between collisions, increasing thermal agitation of the molecules results in a larger viscosity. This transfer of momentum can be thought of as a frictional force between layers of flow. Viscosity in gases arises from molecules traversing layers of flow and transferring momentum between layers. The formulas given are valid only for an absolute temperature scale therefore, unless stated otherwise temperatures are in kelvins. Here dynamic viscosity is denoted by μ \mu and kinematic viscosity by ν \nu. Engineering problems of this type fall under the purview of tribology. Understanding the temperature dependence of viscosity is important for many applications, for instance engineering lubricants that perform well under varying temperature conditions (such as in a car engine), since the performance of a lubricant depends in part on its viscosity. This article discusses several models of this dependence, ranging from rigorous first-principles calculations for monatomic gases, to empirical correlations for liquids. In liquids it usually decreases with increasing temperature, whereas, in most gases, viscosity increases with increasing temperature. Viscosity depends strongly on temperature.
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