Question

Why does coefficient of viscosity decrease with increase in temperature in liquids?From F=6piR eta v or F=eta Adv/dx,viscous force is proportional to coeffocient of viscosity.But,this does not stand true if coefficient of viscosity decreases with increase in temperature?

Solution

With an increase in temperature, there is typically an increase in the molecular interchange as molecules move faster in higher temperatures. The gas viscosity will increase with temperature. According to the kinetic theory of gases, viscosity should be proportional to the square root of the absolute temperature, in practice, it increases more rapidly. In a liquid there will be molecular interchange similar to those developed in a gas, but there are additional substantial attractive, cohesive forces between the molecules of a liquid (which are much closer together than those of a gas). Both cohesion and molecular interchange contribute to liquid viscosity. The impact of increasing the temperatureof a liquid is to reduce the cohesive forces while simultaneously increasing the rate of molecular interchange. The former effect causes a decrease in the shear stress while the latter causes it to increase. The result is that liquids show a reduction in viscosity with increasing temperature. With high temperatures, viscosity increases in gases and decreases in liquids, the drag force will do the same. Impact of Increasing Temperature The impact of increasing temperature will be to slow down the sphere in gases and to accelerate it in liquids. When you consider a liquid at room temperature, the molecules are tightly bound together by attractive inter-molecular forces (e.g. Van der Waal forces). It is these attractive forces that are responsible for the viscosity since it is difficult for individual molecules to move because they are tightly bound to their neighbors.

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