University of Virginia
Physics Department

## Mixing Warm and Cold Water

A Physical Science Activity

Adapted from Experiment 7: Mixing Warm and Cold Water in Physical Science with CBL published by Vernier Software

2003 Virginia SOLs

• PS.1
• PS.7

Objectives

The student will

• use the TI Graphing Calculator, CBL System, and temperature probes;
• construct and use a simple calorimeter;
• mix cold and warm water and determine the heat gained or lost from each.

For information on how to obtain the calculator software necessary to perform this experiment, click here.

Motivation for Learning

Temperature Trick or The Importance of Thermometers

Materials

• Three large bowls (or buckets), large enough to put your hands in.
• Hot water (can be from the tap: not boiling hot) and cold water

Procedure

1. Fill one of the bowls with the hot water, one with the cold water, and pour equal amounts of hot and cold water into the third bowl. Don't let the students see or know what you have done. This should be done in advance.
2. Have a student come forth and put one hand in the warm water and one in the cold water for 30 seconds
3. Now ONE HAND AT A TIME have the student put his/her hands in the in-between bowl of water. Ask the student what they feel. The hand that was in the hot water will sense cold, and the hand that was in the cold water will sense hotness. The water is hot and cold at the same time!

Background Information

The water in the bowl is the same temperature throughout, but it feels different for each hand. This is because our sense of temperature depends on where our body has been. Thermometers are better at determining temperature, but even they must have time to come to equilibrium, and a thermometer with large mass may change the temperature of the object that it is measuring.

When a hot object is put into contact with a colder object, the hot object will loose energy to the colder object. This transfer of energy is referred to as heat. Different materials transfer heat in different ways depending on their physical properties. In addition, the mass and temperature of the substance affect the transfer of heat. This transfer of heat is measured using a calorimeter. In this lab, a calorimeter will be constructed from a Styrofoam cup inside a beaker with the temperature probe used to measure and record the temperature. The Styrofoam helps limit the loss of energy (i.e. heat energy) to the air surrounding the substance. The calculation that can be done to find the change in heat energy Q is:

Q = DT * m * c

where DT is the change in temperature, m is the mass, and c is the specific heat capacity constant of the particular object. In this experiment, the student will practice using a calorimeter he or she constructs to measure heat transfer.

### Student Activity

Materials (for each group of 3)

• CBL system
• TI-83 graphing calculator
• 2 Vernier temperature probes
• Styrofoam cup
• 250-mL beaker
• Cold water
• Warm water
• Stirrer

Procedure

1. Put your safety goggles on. NOTE: Goggles should be worn throughout the activity.
2. Plug in the first temperature probe into the first CBL input, and the second temperature probe into the second CBL input.
3. Run the Vernier program PHYSICS on the calculator.
4. Set up the calculator and CBL unit for two temperature probes, one in channel one and the other in channel two.
5. To setup the calculator for data collection:
1. Change the data collection speed by selecting COLLECT DATA from the main menu, then select TIME GRAPH from the data collection menu.
2. Enter 2 as the time between samples, in seconds
3. Enter 45 as the number of samples
4. Press enter, then select USE TIME SETUP to continue.
5. Select LIVE DISPLAY
6. Enter 0 as the minimum temperature (Ymin)
7. Enter 50 as the maximum temperature (Ymax)
8. Enter 5 as the temperature increment (Yscl)
6. Construct a calorimeter by placing a Styrofoam cup into a 250-mL beaker.
7. Measure 50 mL of cold water with a graduated cylinder and pour this into the calorimeter. Put probe 1 in the cold water.
8. Measure 50 mL of warm water using the graduated cylinder and leave this water in the cylinder. Put probe 2 into the graduated cylinder.
9. The probes must be in for at least 45 s to measure the correct temperature. When the probes have been in for that time, start data collection.
10. After the first few readings are made, pour the warm water into the Styrofoam cup also transferring the probe. Stir with stirrer until the data collection is complete.
11. Proceed to the graph displaying the curves by pressing ENTER. At SELECT GRAPH, choose option 3, BOTH to display probes 1 and 2 on the same graph. Press ENTER. Observe that they both converge on the same temperature, because the temperature in the Styrofoam cup at the end is at only one temperature. Find the maximum and minimum values that were found for Probe 1 and Probe 2 and record. Use the up and down arrows to move from the probe 1 graph to the probe 2 graph.

Data Sheet

 Cold Water (Probe 1) Hot Water (Probe 2) Minimum Temperature (°C) Maximum Temperature (°C) Change in Temperature DT (°C)

1. Calculate the heat gained by the cold water and the heat lost by the hot water by the equation:
Q = DT * m * c
where m = 50 g of water and c = 4.184 J/g°C for water.

2. Calculate the percent difference of the heat gain and the heat loss:
% Difference = [(heat lost - heat gained)/ heat lost] * 100

Questions:

1. Right after combining and stirring the hot and cold water with the two thermometers, the thermometers read two different temperatures. Why? They are right next to each other in the container!

2. Why is there a difference in the amount of heat that is lost and gained in the system? What are some of the factors that may have caused this difference?

1. The temperature probes can't instantaneously read a different temperature. This is because, for the hot thermometer, it takes a while for it to cool down, and for the cool thermometer, it takes a while for it to heat up. This is what we are seeing when we graph the change in temperatures right after the hot and cold water are mixed.
2. The possible factors that could affect this reading are heat exchange with the room, error in measuring temperature, and error in measuring water volume. The heat lost should equal the heat gained.

Students with Special Needs

All students should be able to participate in this activity.

Click here for further information on laboratories with students with special needs.

Assessment

Data sheet and Questions to be completed during the laboratory.