Define the coefficient of viscosity. Use kinetic theory to show that the coefficient of viscosity of a gas is given, with suitable approximations, by
η=Kρ⟨c⟩λ
where ρ is the density of the gas, λ is the mean free path of the gas molecules, ⟨c⟩ is their mean speed, and K is a number that depends on the approximations you make.
In 1660 Boyle set up a pendulum inside a vessel that was attached to a pump that could remove air from the vessel. He was surprised to find that there was no observable change in the rate of damping of the swings of the pendulum when the pump was set going. Explain his observation in terms of the above formula.
Make a rough order-of-magnitude estimate of the lower limit to the pressure that Boyle obtained; use reasonable assumptions concerning the apparatus that Boyle might have used. [The viscosity of air at atmospheric pressure and at 293 K is 18.2μN s m−2.]
Explain why the damping is nearly independent of pressure despite the fact that fewer molecules collide with the pendulum as the pressure is reduced.