Outline of Theory

In this section we present relations between the moment of inertia (J), of the rotational pendulum and measurable parameters of its slow, damped harmonic oscillations, namely the frequency (co) and the logarithmic decrement (A). As the geometry of the pendulum normally is known, from these relations, set up for oscillations in both vacuum and in a sorptive gas atmosphere, the mass of the pendulum and hence the mass of an adsorbed phase included in it can be calculated - at least in principle. 

The equation of motion of the rotational pendulum loaded with sorbent material (m ) is [5.1,5.2]  

Here a = o(t) is the angular displacement or amplitude of the pendulum, the dot ( ) indicating the time derivative. The moment of inertia (Jo) consists of two parts 

The retarding moment (Do) of the torsional wire included in the equation of motion (5.1) can be calculated from the wire s length (L ), its diameter (2r ), the elasticity modulus (E) and the Poisson number ( ) by the relations [5.2, 5.3] 

The coefficient of internal damping of the wire (Ro) included in Eq. (5.1) in practice must he determined from calibration experiments with either the empty or the loaded pendulum in vacuum, cp. Eq. (5.12). Experiments have shown that (Ro) may change over the years which can be due to irreversible plastic deformation or corrosion if measurements in chemically aggressive sorptive gases have been performed [5.2]. 

---

Spiegel, Murray R. Schaum s Outline of Theory and Problems of Advanced Calculus, McGraw-Hill Book Company, New York (1963). 

Hall/CRC, New York (2004) Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 2d ed., CRC Press, New York (2002) Wrede, R. C., and Murray R. Spiegel, Schaum s Outline of Theory and Problems of Advanced Calculus, 2d ed., McGraw-Hill, New York (2006) Zwillinger, D., CRC Standard Mathematical Tables and Formulae, 1st ed., CRC Press, New York (2002) http // eqworld.ipmnet.ru/. 

Gifford, F. A. (1968). An outline of theories of difiusion in the lower layers of the atmosphere. In Meteorology and Atomic Energy (D. Slade, ed.), USAEC TID-24190, Chapter 3. U.S. At. Energy Comm., Oak Ridge, Tennessee. 

Schaum s Outline of Theory and Problems of ORGANIC CHEMISTRY... 

Schaum s outline of theory and problems of organic chemistry / Herbert Meislich. Howard Nechamkin. and Jacob Sharefkin. -- 2nd ed. p. cm. -- (Schaum s outline series)... 

Kuchel, P.W., Ed., Schaum s Outline of Theory and Problems of Biochemistry, McGraw-Hill, New York, 1998. Lea, P.J. and Leegood, R.C., Eds., Plant Biochemistry and Molecular Biology, 2nd ed., John Wiley Sons, New York, 1999. 

Moser, C. C., and Dutton, P. L., 1996, Outline of theory of protein electron transfer. In Protein Electron Transfer (D. S. Bendall, ed.) pp. In22, BIOS Scientific Publishers Ltd. Oxford, U.K. 

Outline of Theory and Problems in College Chemistry, D. Schaxim, C. O. Beckmann, H. Mouquin, and J. I. Rosenberg, Schaum Publishing Co., New York, 1949. 

Morgan s Outline of Theory of Solution and its Results.xamo. 

General Reeerences Abbott, M. M., and H. C. Van Ness, Schaum s Outline of Theory and Problems of Thermodynamics, 2d ed., McGraw-Hill, New York, 1989. Poling, B. E., J. M. Prausnitz, and J. P. O Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001. Prausnitz, J. M., R. N. Lichtenthaler, and E. G. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 3d ed., Prentice-Hall PTR, Upper Saddle River, N.J., 1999. Sandler, S. I., Chemical and Engineering Thermodynamics, 3d ed.. 

---