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Calorimetric measurements of weakly absorbing materials: theory

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Abstract

The time-dependent heat equation is solved in a cylindrical geometry of finite length with heat loss by radiation and conduction. Exact expressions are derived for the time constants of radial and longitudinal modes. The steady-state solution is obtained in longitudinal modes and used as the initial state for the decay. A simple expression is presented for the ratio of the amplitude of the first-order longitudinal order mode A1 and the corresponding time constant τ1 fit with the separate expressions for A1 and τ1. These parameters are experimentally readily accessible and directly yield the absorption coefficient α of rod-shaped compound glass from which optical fibers are to be drawn.

© 1979 Optical Society of America

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