2. The viscosity of a liquid can be calculated using the Stokes-Einstein equation
\(\eta = \frac{kT}{6\pi rD}\)
where \(\eta\) is the viscosity, k is the Boltzmann constant (1.38 × 10?²³ J/K), T is the absolute
temperature, r is the molecular radius, and D is the self-diffusion coefficient (m²/s).
a. Determine the unit of viscosity, \(\eta\), by doing a dimensional analysis based on the Stokes-
Einstein equation. Show work.
b. Show that the unit you derived in part (a) is the same as the SI unit for viscosity: kg/(m·s).
c. Find the conversion factor between the unit you derived in part (a) and the more commonly
used unit for viscosity, cP (centiPoise). 1 Poise = 1 g/(cm·s).
d. Express a viscosity of 0.306 cP in the SI unit.