Graphical representation for thermal equilibrium when transition temperatures are present

Abstract

We propose the use of graphics in order to get a quick insight of the thermal equilibrium of two bodies, when a transition temperature is present in the interval between both initial temperatures. We have found two convenient variables in order to represent the mathematical condition for the partial or complete transition of each component. In mixing hot water and cold ice, the proposed graphical representation exhibits straight lines separating four regions corresponding to different equilibrium states, going from one containing just ice up to the other containing just water, and two states in between with increased ice or increased water. This graphical representation helps to avoid typical student errors in learning elementary physics.