Extension Activity: Some Like It Hot!

Major Chemical Concept

When samples of water at different temperatures are mixed, the final temperature of the mixture will have a value that lies between that of the hotter sample and the colder sample. According to the laws of thermodynamics, heat flows from warmer into cooler bodies. The warm water cools down and the cool water warms up. The process continues until a uniform temperature is reached at which time the temperature change ceases. It is quite a simple task using algebra and graphical analysis to find the quantitative relationship that relates the final temperature of the mixture to the initial temperatures of the cold and hot samples, respectively.

Level

Mainstream, first-year high school chemistry. Introductory level for all students.

Expected Student Background

See Related Concepts and Related Skills. Graphing skills and ability to transfer graphical information into an appropriate algebra expression are essential.

Time

Teacher preparation: 15 min

Student laboratory time: Approximately 50 min

Safety

Read the Safety Considerations in the Student Version. Normal safety precautions when using hot water should be observed. There are no chemical hazards.

Materials

(For 24 students working in pairs)

24 Styrofoam Ò cups

24 Graduated cylinders, 100-mL

12 Thermometers calibrated in °C

12 Sections of rubber tubing to use with thermometer

24-36 Sheets of graph paper

12 Pencils

12 Rulers

Insulated coolers or coffee urn (2 or 3 for the class)

Advanced Preparation

Decide upon the type of hot water containers to be used and secure them before the laboratory time. Also, the teacher should remind the students to bring a calculator to the laboratory session.

Pre-Laboratory Discussion

By the nature of the exercise which uses Piagetian strategies, very little advanced discussion should be necessary. Just encourage the students to get to work on the activity and discover the existing relationships between the hot and cold water.

Teacher-Student Interaction

The teacher should circulate throughout the laboratory and assist the students in drawing and interpreting the graph of the hot, cold and mixture of water

Anticipated Student Results

Some students will be unable to derive a relationship to find the final temperature of a mixture of hot and cold water from the data alone. In such instances, have these students make the graphs and find the areas before deriving a relationship or an algebraic formula. Some students may be able to derive a relationship from the data. In such cases have them make the graphs to confirm the formulas before you give them a set of data to check their algebraic formula.

Below is a sample of a set of data to check the algebraic formula.

Actual temperatures of water kept in the insulated cooler or coffee urn can be quite different from student predictions based upon their laboratory experiment. This discrepancy is due to experimental design problems. Students often measure the hot water into a graduated cylinder directly and then pour it into the cup of cold water prior to taking the temperature. Consequently there may be considerable heat loss depending on delay of student work. This presents the instructor with an opportunity to discuss design of experiments. Several options are available depending on the instructorÕs inclination. One viable option is to have students brainstorm a new experimental procedure and repeat the laboratory on a subsequent day.

One procedure to produce better accuracy is to measure the volume of cold water with a graduated cylinder and add it to a Styrofoam Ò cup. Determine the temperature of the cold water and record it. Add hot water directly to the Styrofoam Ò cup and measure the temperature of the mixture after brief mixing. Be sure not to add too much hot water because the thermometer is covered beyond the 40 °C mark. Next, determine the final volume of the mixture using a graduated cylinder. Subtract the colder water volume from the mixture to find the hot water volume. Now substitute the variables into the algebraic equation and solve for temperature of the hotter water.

Answers to Data Analysis and Concept Development

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