Molecular Theory of the Viscosity of Gases Scientists have placed 1 mole of a mo

Question

Molecular Theory of the Viscosity of Gases

Scientists have placed 1 mole of a monoatomic gas [molecular weight = 12, 3 A diameter) in a cubic tank of length 1 m. Experiments indicate that all molecules in the tank move with a uniform molecular velocity of 500m/sec at room temperature (an idealized assumption). Calculate (A) the pressure on a wall of the tank at room temperature, (B) the mean free path between molecular collisions, (C) the viscosity of the gas (the expression for viscosity in your notes is and (D) whether increasing temperature increases or decreases the viscosity. Give units for all these quantities calculated.

Explanation / Answer

part 1 :

pressure on walls = n RT/V

  

n = 1, T = 298 k room temp. V = 1x1x1 = 1 m^3 = 1000L

P = 1x0.0821 x 298/1000 = 0.0245 N/m2

part 2:

mean free path between collisions = Vavg / Z

  

Vavg = 500m/sec

  

Z = frequency between collision = pi*D^2 x Vrms X N/V

z = 16.22 m/sec.

mean free path between collisions = 500 /16.22 = 30.83 m

part 3:   

viscosity = 2nv/9 xmxmean free path

= 82.21 N

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