Mathematical treatment of heat flow in differential scanning calorimetry and differential thermal analysis instruments

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Abstract
A general mathematical treatment is given which relates the techniques of classical differential thermal analysis, power‐compensated differential scanning calorimetry, and heat‐flux differential scanning calorimetry. An idealized system, representative of almost any type of differential thermal instrument, is presented, which, unlike those of previous treatments, incorporates two separate thermal resistances. This modification allows the heat‐flux d.s.c. instrument to be considered in a unified analysis with the other techniques. General aspects of the idealized system are presented, and the equations governing heat flow within the system are developed. For each separate technique, the components of the idealized system are identified with the actual components of the physical instrument, and the specific equations which describe the measuring principles of that technique are derived. It is shown that a similar type of thermal resistance governs sample‐temperature lag in both the power‐compensated and heat‐flux d.s.c. cases, and the method of estimating the value of this resistance from the slope of a fusion peak is discussed.

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