Extension Activity: Some Like It Hot!

Introduction

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.

Purpose

Your task is to find the quantitative relationship that relates the final temperature of the mixture to the initial temperatures of the cold and hot samples, respectively.

Safety

1. Wear protective goggles and apron throughout this laboratory activity.

2. As always when working with hot water, be careful not to come in contact with the hot water or the hot containers in which it is held. Move all hot objects with beaker tongs or a hot pad.

Procedure

1. Use the following procedure to mix measured volumes of hot and cold water. As a guide, be sure that the final volume of the mixture is between 100 mL and 150 mL.

2. Place a measured volume of cold water, as determined by using a graduated cylinder, into one Styrofoam Ò cup.

3. Place a measured volume of hot water into the other Styrofoam Ò cup.

4. Measure the temperatures of the cold water, and the hot water, to the nearest 0.2 °C.

5. Pour the contents of one cup into the other cup, and measure the temperature of the mixture.

6. Record the data into a table similar to the one below.

7. Repeat the experiment two more times using different volumes of hot and cold water.

8. Use the data to help you formulate a rule that will allow you to predict the temperature of the final mixture. If you have a rule, share this with your instructor, who will ask you to predict the temperature of a mixture you have not investigated.

9. Whether or not you have established a valid rule, the second task of this experiment is to use the data from one of your three trials to construct graphs. From the selected trial, make three graphs using the temperature of the sample versus the volume of the sample for the cold, hot, and hot and cold mixture, respectively. To make the graphs, plot a single point (e.g., Volume Cold, Temperature Cold) on the graph paper. Construct a rectangular area by drawing the respective lines going to the x and y axis. Be sure to use the same increments on the axis scale for each graph.



Figure 20. Sample for 20 mL of 40 °C water mixed with 40 mL of 10 °C water.

10. Using the axis readings determine the area of each rectangle. Find a relationship between the sum of the area associated with the hot and cold water and the area associated with the mixture.

11. Answer Questions 1 to 3 from the Data Analysis and Concept Development section based upon your data and observations so far.

12. The third task is to put your rule to a laboratory test. First prepare a thermometer by partially covering it with black paint or paper or opaque rubber tubing. Carefully slide the tubing over the top portion of the thermometer, leaving the lower portion of the thermometer exposed up to the 40 °C range. (This will prevent the student from measuring directly the temperature of the water in the coffee urn.) There will be a source of hot water in the laboratory in a coffee urn or insulated cooler. You are to determine the temperature of this hot water in the container by indirect means. Take some time to plan the procedure of this aspect of the experiment. Plan to do at least three trials.

13. Finally, check with your instructor and compare the actual temperature with your prediction. Discuss how the experimental design could be improved to increase accuracy. You may test your new design by repeating the experiment.

14. Answer Questions 4 to 7 in the Data Analysis and Concept Development section.

15. Thoroughly wash your hands before leaving the laboratory.

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