Derivation of temperature variation rule and variation rules of temperature lag, heat flows, internal energy and effective specific heat of platelike sample in temperature modulated differential scanning calorimetry

Abstract In this paper, the temperature variation rule of platelike sample in temperature modulated differential scanning calorimetry (TMDSC) has been drawn with strict mathematical derivation. The obtained analytical result reveals the total variation rule of the platelike sample from its initial equilibrium state to its steady state. With this temperature variation rule, the variation rules of both reversible and irreversible heat flows, temperature lag, internal energy and effective specific heat of the platelike sample have been derived and studied as well. If the thermal conductivity of the sample is so great that the temperature gradients within the sample can be neglected, in this case the temperature variation rule derived from the fundamental equation of the temperature distribution of our TMDSC is the same as the current TMDSC theories. If the modulated amplitude A T s or modulated frequency ω equals zero, it reverts to the conventional DSC situation, so all the results in the TMDSC model derived in this article are automatically suitable for the conventional DSC situation and current TMDSC theories.