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.