Page 257 - Gas Adsorption Equilibria

5. Oscillometry 243

These relations can be used to calculate numerically and from measured
data and which is known from wire’s geometric and
thermophysical data via equations (5.4-5.6).

For the motion of the empty pendulum in vacuum we have
analogously to (5.1) the equation of motion

leading for the same initial conditions as above to the amplitude function

and correspondingly to (5.11), (5.12) to the relations

Hence we get by dividing equations (5.12) and (5.16) for the ratio of the
moments of inertia the expression

which can be determined from (calibration) measurements of the empty (L)
and the loaded (0) pendulum in vacuum.

2.2.2 The Motion of the Pendulum in Sorptive Gas

The motion equation of the rotational pendulum loaded with sorbent of
mass in a gaseous atmosphere is [5.1]:

The moment of inertia (J) of the pendulum can be written as