In this session, we will mix three or more equal volumes of water at different temperatures and measure the temperature of the final mixture. We will extend this experiment to include cases where at least two of the equal volumes of water are the same temperature. Then we will extend the experiment to allow for different masses and different temperatures.
We want the student to become familiar with the concept of "weighted mean". In this context, weighted mean will allow the students to calculate the final temperature of a mixture of water from several containers, each with a different temperature and a different mass. We want the student to recognize that a hypothesis and theory must often be modified to take into account new facts or to extend the hypothesis. Also we hope to keep the scientific method, experimental technique, and errors before the student.
Begin by serving hot and cold drinks again. This time, cool your coffee using equal volumes of cold and hot coffee. This demonstration can be pretty ridiculous and funny while trying to get coffee to the right temperature.
Encourage students to devise a hypothesis and mathematical expression for predicting the temperature of a mixture of several equal volumes of water at different temperatures. Have them test their hypothesis.
Then ask the students to modify/simplify the expression for two or more of the containers to have water of the same temperature.
Finally ask the students to modify the expression to allow different volumes at different different temperatures. The wise instructor will encourage the students to change from volume to mass because mass will be must easier to handle experimentally. The students should test this new expression experimentally.
Ask the students to evaluate their experimental procedure, discuss their errors, and devise a better way to perform the experiments.
The following graph indicates one way in which the students could perform their experiments. Using the technique implied by the graph, the students could add small known mass of water of a known temperature to a mixture and measure the resulting equilibrium temperature. The end points of this graph repeat the experiment in the previous lesson.
Create a problem set that reviews the classroom procedure.