Page 261 - Gas Adsorption Equilibria

5. Oscillometry 247

two linear algebraic equations from which both the Laplace transform of the
torque (M(t)) and the moment of inertia (J) of the pendulum can be calculated
if the amplitude of the pendulum has been determined experimentally.
As the relaxational motions of the pendulum for small amplitudes
can be described by a damped harmonic oscillation, we have

the index “E” at the frequency and the decrement of the oscillation
indicating “experimentally determined”. By this reasoning we get for the ratio
of the moments of inertia J and the expression [5.1, 5.2]:

Hence we have for in view of (5.17), (5.25) and (5.38)

Thus we recognize that in order to determine the relative increase of the
mass of the pendulum due to gas adsorption as defined by the l.h.s. of (5.25),
three types of measurements are necessary leading to the characteristic
quantities of

the motion of the empty disk in vacuum
the motion of the disk filled with sorbent in vacuum
the motion of the disk filled with sorbent in in sorptive gas

Once is known from Eq. (5.39), the mass adsorbed can be
calculated from (5.25). The sorptive gas mass included in for pellet-
like sorbents has to be calculated via the helium-volume of the sorbent
material from the relation