1.

In an experiment on Brownian motion, using a torsion pendulum (a small mirror of area 1 mm2 mounted on a thin torsion fibre with torsion constant = 1.8 x 10-17 J/rad2 the mean value of angular displacement θ was found to be nearly zero, and the fluctuation in θ, that is the mean square of θ was found to be 2.6 x 10-4 rad2. Estimate the value of Boltzmann's constant from this data and compare it with the correct value. The temperature is 300 K.

Answer»

Here, torsion constant, C = 1.8 x 10-17 J

<θ2> = 2.6 x 10-4 rad2, and T = 300 K

Using the relation: 1/2 kBT = 1/2 C <θ2>

⇒ kB = {c<θ2>}/{T}

= {1.8 x 10-7 x 2.6 x 10-4}/{300}

= 1.56 x 10-23 JK-1

This value is different from the actual value of Boltzmann's constant, i.e., 1.38 x 10-23 J K-1.


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