Calorimetric measurements of weakly absorbing materials: theory

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 A(1) and the corresponding time constant tau(1)fit with the separate expressions for A(1) and tau(1). These parameters are experimentally readily accessible and directly yield the absorption coefficient alpha of rod-shaped compound glass from which optical fibers are to be drawn.