In each of the preceding sessions, the final equilibrium temperature of a mixture is some kind of an average of the initial temperatures. However, we have seen a situation where that is not true. When heat is added to ice, the ice melts and the temperature of the ice/water mixture is constant. In this lesson we will investigate that situation.
We hope to discover a way to measure the amount of ice that melts under controlled circumstances. We hope to be able to predict the amount of melt based on repeatable experimental circumstances.
Begin by repeating demonstration where we heat ice in a beaker and record its temperature as a function of time. The water remains at the freezing point until all the ice has melted. Ask the students to characterize what they see. Ask them to devise some measurement technique to measure the amount of ice that melts in terms of some other controllable quantities.
Our hope is that the students will realize that the same mixing techniques we have used previously can be modified to melt the ice in a measurable way. That is, putting a measured quantity of hot water in ice will melt the ice in a predictable way.
When the students discover the measurement technique, ask them to make several measurements, and create an appropriate graph. Then ask them to create a conjecture about how to predict the amount of ice that will melt when a given amount of water at some temperature is added to the ice. Actually, the students should struggle with this a little more so don't be too forthcoming with suggestions.
Ask the students to pay particular attention to the scientific method and experimental technique. They need to be aware of several things:
If the students need a stronger hint, ask them to write an equation with the initial state of the system on the right and the final state of the system on the left. This equation is probably not the answer but a place to start thinking about the problem. The students need to come to the realization that something new is happening. That is, the ice is changing to water by adding warmer water, but the temperature of the ice and water does not change. In fact the warmer water cools. The graph of the experimental results should provide a strong hint that the weight of the melted ice is proportional to both the weight and temperature of the added water. After staring at this equation for a while, the students should decide that some of the terms should be used in some different way. Make the required changes. Then "solve" that equation so that the independent variable is on the right with all its factors and terms. The dependent variable should be on the left all alone. A sanity check is to make sure the equation can duplicate the experimental graph. The equations of interest are shown below with m as the mass, T as the temperature, and the dual subscripts mean "ice final", "ice initial", "water final", and "water initial" in the expected way.
The hypothesis in this situation is going to be a little more complex. Again, devise a short problem set that will lead them to the hypothesis extension. Introduce the term "latent heat of fusion".
The problem set should also extend the idea to "latent heat of vaporization". The problem set should describe an experiment in which steam is used to heat cold water. The change in temperature of the cold water will be proportional to the weight of the steam used to heat it. From this situation, we can extend the students' hypothesis to a second type of "latent heat".
The problem set will be critical in this session. It will solidify the contents of the classroom experiments, introduce vocabulary, and provide a framework for extensions to the idea of "latent heat".
Suggested problems