VISCOSITY of a GAS -Dr S P Singh Department of Chemistry, a N College, Patna
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Lecture Note on VISCOSITY OF A GAS -Dr S P Singh Department of Chemistry, A N College, Patna
A sketchy summary of the main points
Viscosity of gases, relation between mean free path and coefficient of viscosity, temperature and pressure dependence of viscosity, calculation of collision diameter from the coefficient of viscosity
Viscosity is the property of a fluid which implies resistance to flow. Viscosity arises from jump of molecules from one layer to another in case of a gas. There is a transfer of momentum of molecules from faster layer to slower layer or vice-versa. Let us consider a gas having laminar flow over a horizontal surface OX with a velocity smaller than the thermal velocity of the molecule. The velocity of the gaseous layer in contact with the surface is zero which goes on increasing upon increasing the distance from OX towards OY (the direction perpendicular to OX) at a uniform rate . Suppose a layer ‘B’ of the gas is at a certain distance from the fixed surface OX having velocity ‘v’. Two layers ‘A’ and ‘C’ above and below are taken into consideration at a distance ‘l’ (mean free path of the gaseous molecules) so that the molecules moving vertically up and down can’t collide while moving between the two layers.
Thus, the velocity of a gas in the layer ‘A’ ------(i) = + Likely, the velocity of the gas in the layer ‘C’ ------(ii) The gaseous molecules are moving in all directions due= to −thermal velocity; therefore, it may be supposed that of the gaseous molecules are moving along the three Cartesian coordinates each. Consequently, of the total molecule will be moving upward and of the molecules will be moving downward the layer ‘B’ at any instant. There is thus, a continuous interchange of molecules between the ℎ layers A and C. ℎ Let, n = no. of molecules per cc m = mass of each gaseous molecule = average velocity of the gas