The viscosity of a gas is directly proportional to?
Answers
Answer:VISCOSITY OF GASES
1. Introduction
Fluid flow through pipes is of immense importance to chemical engineers, who must design appropriate methods for transporting chemicals to and from reaction vessels. Viscosity of fluids is the key physical property that dictates the design of pipelines to transport material. Thus, an understanding of liquid and gas viscosity is essential for engineering a chemical process.
The viscosity of gases played an important role in the historical development of the kinetic theory of gases (see Keith J. Laidler, The World of Physical Chemistry, Oxford University Press, 1993, p. 150-154). James Clerk Maxwell, who is famous for the Maxwell-Boltzmann distribution of molecular velocities and Maxwell's Equations of electromagnetic radiation, proposed in 1860 that gases possess a distribution of velocities. Although now fully accepted, this proposal went against the conventional theory of the time that a range of velocities would be equalized by molecular collisions. He was troubled with his own proposal, however, because it had "the curious result" that viscosity is independent of pressure which was "certainly very unexpected." Maxwell and his wife made the first reliable measurements of gas viscosities in order to determine the dependence of gas viscosity on temperature and pressure. These measurements were made using an apparatus in attic of their house, and the temperature was controlled through appropriate stoking of the fireplace. The results were reported in 1866, reconciling his kinetic theory of gases with observed gas viscosities.
As an aside, Maxwell was never able to reconcile his kinetic theory of gases with the observed ratio of specific heats, Cp/Cv, for diatomic gases. A diatomic molecule has three translational, three rotational, and one vibrational degree of freedom. Translational and rotational degrees of freedom each contribute 1/2 R to the specific heat, and vibrational degrees of freedom contribute R to the specific heat. Since Cp = Cv + R, the ratio of specific heats was predicted to be (3/2R + 3/2R + R + R) / (3/2R + 3/2R + R) = 5R / 4R = 1.2, which differed from observed values for oxygen, hydrogen, and nitrogen of about 1.4. As a result, Maxwell proclaimed that the kinetic theory "could not possible satisfy the known relation between the two specific heats of a gas" and "the result of the dynamical theory, being at variance with experiment, overturns the whole hypothesis, however satisfactory the other results might be." Despite considerable effort, Maxwell was never able to reconcile the kinetic theory of gases with the specific heats experimental result. This required the advent of quantum mechanics, which explained that the degrees of freedom for molecular vibration and rotation around the axis of a linear molecule were to be neglected because the excited quantum states for these motions were too high in energy to be accessed at room temperatures. Thus, the ratio of specific heats should be (3/2R + 2/2R + R) / (3/2R + 2/2R) = (7/2R) / (5/2R) = 1.4, which is in very close agreement with experiment.
Both gas effusion and gas viscosity experiments validate the kinetic theory of gases and provide access to microscopic information from macroscopic measurements. The rate of gas effusion provides a means of determining the average molecular velocity, as faster molecules will strike the pinhole area more frequently and therefore effuse more rapidly. The viscosity of a gas provides a means for determining molecular diameters, as viscosity arises from collisions among molecules.