Answer to Question #89768 in Molecular Physics | Thermodynamics for Shivam Nishad

Question

Discuss the significance of Brownian motion in kinetic theory of gases. Obtain the expression for particle concentration in sedimentation process. The motion of soot particles of radius 0.5 x 10^-4 cm in water-glycerine solution characterized by n= 2.80 x 10^-3 kg m^-1 s^-1 at 300 K was observed
for 10 s. The observed value of ∆(x² ) was
3.30 x 10^-8 cm². Calculate Boltzmann
constant.

Answer 1

Kinetic theory of gases is a theory based on a simplified molecular or particle description of a gas. Brownian motion is the random motion of particles resulting from their collision with the fast-moving molecules in the fluid. This motion is named after the botanist Robert Brown, who was the most eminent microscopist of his time. In this way, the Brownian motion is an experimental confirmation of kinetic theory of gases.

According to the Einstein's theory of Brownian motion of molecules, we can write

$$\frac { x^2}{2t} =\frac {kT}{6 \pi n r} (1)$$

Using (2) we can write

$$k=\frac { 3 \pi n r x^2}{t T} (2)$$

We got:

k=1.45×10^-23 J/K