A rigorous method for the preliminary analysis of the valid temperature range in calorimetry problems involving phase changes

Abstract

In the undergraduate teaching of heat exchange problems between hot and cold substances (calorimetry), the principle of conservation of energy (heat, in this case) is the key for solving such problems. For some years now, probably to associate the concepts of “system'' and ”environment'' with the signs of heat, the equation for the conservation of heat energy is usually written ∑Q_i=0. In the work that we are going to present, it is better (even necessary) to go back to the “old'' way of writing that conservation of heat energy with the expression  , so that the heat is written with a positive sign on both sides of equality. Our work is novel because it introduces a rigorous path (not used in the bibliography) when calculating the final temperature of the hot-cold mixture, when the range between T_hot,initial and T_cold,initial includes phase change temperatures in any of the substances that are mixed. To those cases in which a phase change is possible, we also introduce a use of the temperature-heat diagram in a way that is also partly novel, which will be very useful for the analysis prior to obtaining the final equilibrium temperature.