The purpose of this lab experiment is to measure the specific heat capacity of unknown metal samples and also to determine the latent heat of fusion of water. In addition, we will study the effectiveness of different calorimeters.

When energy in the form of heat, , is added to a material, the temperature of the material rises. Note that temperature, in units of degrees Celsius (°C) or Kelvin (K), is a measure of how hot or cold a substance is, while heat, in units of joules (J) or calories (cal), is a measure of its thermal energy. 1cal = 4.19J.

Specific Heat

A measure of the efficiency with which a substance can store this heat energy is known as specific heat capacity, or simply the specific heat, . The greater the material's specific heat, the more energy must be added to change its temperature. As an example, the specific heat of water is given as , which means that 1.00 calorie of heat is necessary to raise one gram of water one degree Celsius, or 4190 joules of heat are necessary to raise one kilogram of water one Kelvin. Specific heat values for various other materials are listed in Table 1 below.

The heat necessary to cause a temperature change, , in a material of mass, , is given by the equation

(1)

where is the specific heat capacity of that material. As usual, the change in temperature of the substance is the difference between its final and initial temperatures, .

Table 1

Specific and Latent Heat Values
	Specific Heat		Latent Heat of Fusion
Material	(cal/g °C)	(J/kg K)	(cal/g)	(J/kg)
Aluminum	0.215	900	94.5	3.96x105
Copper	0.092	385	49.0	2.05x105
Iron	0.107	448	63.7	2.67x105
Lead	0.031	130	5.5	0.23x105
Brass	0.092	385	Unknown	Unknown
Magnesium	0.245	1030	88.0	3.7x105
Zinc	0.093	390	27.0	1.1x105
Styrofoam	0.27	1131	Unknown	Unknown
Air	0.240	1006	N/A	N/A
Water	1.000	4190	N/A	N/A
Ice	0.500	2095	79.7	3.34x105

When two bodies having different temperatures come into contact with each other, heat energy is transferred between the bodies. Take, for example, placing a piece of hot metal into a container of cool water. From experience we know over time that the metal sample will become cooler, while the water and its container will become warmer, until an equilibrium temperature is reached. Put another way, according to the law of energy conservation the total heat energy lost by the metal is the total heat energy gained by the water and container:

(2)

The negative sign is used to maintain our sign convention for heat; we set the hot side to be negative because energy is leaving the hot sample. Equation 2 holds true if no heat is exchanged with the surrounding environment and if none of the materials undergo a phase change.

To isolate this experiment from the environment we will utilize two types of calorimeters: a simple styrofoam cup (Figure 3 below) and a more traditional wooden calorimeter with an aluminum cup insert (Figure 4 below). You will determine the effectiveness of both of these calorimeters in this experiment.

Latent Heat of Fusion

The heat required to completely melt a given mass, , of a substance is given as

(3)

In Objective 3 of this experiment, you are to determine the latent heat of fusion of ice, . Here, you will add some ice cubes to a water bath at room temperature. Heat is removed from the water bath to both melt the ice and warm the melted ice water to an equilibrium temperature. Again, from energy conservation arguments we can write

(4)

Note that while in each experiment, the initial temperatures of each material is different, they end up at the same the final temperature.

Density

A common and simple method of checking your calorimetry results is to calculate the density of your material. If you are having trouble determining the identity of your material based on their specific heat values, often times a quick density measurement can aid you in determining which metal you have in your possession. Density values of some common materials are found in Table 2 below.

Table 2

Density of Various Materials
Material	g/cm3
Aluminum	2.7
Copper	8.96
Iron	7.87
Lead	11.3
Brass	8.4
Magnesium	1.74
Zinc	7.14
Lead	11.3
Water	1.00
Ice	0.917

Prior to the experiment, obtain two samples of the same metal and place them both in a hot water bath. Allow enough time for the samples to reach an equilibrium temperature.

1. With one of your metal samples, use the wooden calorimeter and determine the specific heat, , of the metal sample and ascertain the identity of the metal sample. Note that the calorimeter cup is made of aluminum.

2. Use your other metal sample to determine if a styrofoam cup is a reasonable substitute for the wooden calorimeter. When using the styrofoam cup you may assume that there is no heat lost or gained by the styrofoam cup. That is, we can assume = while = 0 and therefore no heat is transferred to the cup. Is there a way to determine if this is a valid assumption?

3. Obtain a small amount of ice from your instructor and use the styrofoam cup as your calorimeter to determine the latent heat of fusion of ice, .

4. Use density arguments to verify the identity the of your metal sample.

(Figure 1.) Two metal samples. Your lab group will need two pieces of either sample for this experiment. (Figure 2.) The metal samples are heated within a water bath shown here. The apparatus includes a stainless steel container and hot plate. A glass thermometer is used to monitor the temperature of the water bath. The rod and clamp are used to hold the thermometer in place. (See Caution note below!) (Figure 3.) The styrofoam calorimeter. (Figure 4.) A typical wooden calorimeter. The metal cup is made of aluminum. (Figure 5.) The Vernier computer interface and stainless steel temperature probe. The probe is useful for accurately monitoring the temperature of the water contained in the calorimeter. (Figure 6.) A screen shot of the Thermometer program located in the 223 Lab Programs folder on the computer desktop. See the Hints and Cautions section below to learn how to import your screen shots into your lab report. (Figure 7.) A triple-beam balance. (Figure 8.) Wear the hot-hand protector when handling the hot stainless steel container. Ice Paper towels Small beaker Vernier caliper

[Click on images to enlarge.] 1 2 3 4 5 6 7 8

1. Caution!!! The hot plate, stainless steel container and the metal samples are quite likely to be very hot. Handle with care.

2. Caution!!! When determining the density of your metals, allow your sample to cool! Do not handle hot ingots!

3. Caution!!! Do not set books, papers or any other flammable materials close to the hot plates!

4. Caution!!! When using a clamp to secure the glass thermometer, use caution when tightening the clamp so the thermometer does not break.

5. This lab could prove very frustrating and may have to be repeated several times if you do not think through the steps ahead of time. Carefully plan your experimental procedure. Also, perform all your calculations in the lab room before you head home.

6. The software for this lab is located on the lab computer's desktop in a folder labeled Lab Programs.

7. The precision of the temperature probe is given as ±0.2°C at 0°C, and ±0.5°C at 100°C.

8. The temperature software is programmed to record data for only 400s (~6.5 minutes). While this is ample time to make your calorimeter readings, make sure that you put the metal samples in the calorimeter with enough time to make the necessary measurements.

9. When using the Logger Pro software, you can easily examine the value of each data point with your mouse by selecting Analyze and then Examine from the software's menu bar.

10. You may wish to include a screen shot image of the temperature measurements in your lab writeup. To do so, with the image on the screen, press the Print Screen button on the keyboard. This will place the screen shot image into memory. Then open the Paint application from the computer desktop and Paste the image. Paint is a very simple application, but you can alter the size of the image using the Sketch/Skew command from the Image menu. For best results, save the image in the GIF format. The image can then be inserted into your word document.

11. Due to various thermal properties of styrofoam, you may assume that no heat is absorbed or lost by the styrofoam cup calorimeter in any of the experiments. Is this a valid assumption?

12. Be sure to turn off the hot plate when the experiment is completed!

1. Compare the market price of a few metals
2. Using the vernier caliper
3. Clemson Physics Lab Tutorials

Each lab group should download the Lab Report Template and fill in the relevant information as you perform the experiment. Each person in the group should print-out the Questions section and answer them individually. Since each lab group will turn in an electronic copy of the lab report, be sure to rename the lab report template file. The naming convention is as follows:

For example the group at lab table #5 working on the Ideal Gas Law experiment would rename their template file as "5 Gas Law.doc".

These Nudge Questions are to be answered by your group and checked by your TA as you do the lab. They should be answered in your lab notebook.

General Nudges

1. Carefully think out all the steps for these Objectives. What is your experimental procedure for each?
2. When will you begin taking temperature measurements of the calorimeter bath?
3. Should the calorimeter's water bath be stirred during the experiment? Should it be stirred continually? Why or why not?
4. What is the uncertainty of the temperature of the calorimeter bath? That is, what is the precision of the temperature probe?
5. What is the uncertainty in the mass measurements?
6. What are the major sources of error for these experiments? How can these errors be reduced?

1. What quantities are needed to be measured in this Objective?
2. Which equation(s) will you use for this Objective?
3. What is the uncertainty of the temperature of the hot water bath? Remember, the hot water bath temperature is measured with the glass thermometer.
4. How is the initial temperature of the metal samples measured? What steps did you take to insure that this is an valid measurement?
5. How much water will you add to the calorimeter before the metal sample is inserted? What factors enter into your decision?
6. When will you begin taking temperature measurements of the calorimeter bath?
7. How will you reduce the experimental error when transferring the hot metal sample to the calorimeter?
8. How will you know when to stop taking data for this Objective?
9. If the thermometer or temperature probe touches the metal sample or metal container, how will this affect the temperature measurements, if at all?
10. How is determined for each material in this Objective?
11. What is the uncertainty of the measurements?
12. When Objective 1 is completed, should you return the metal sample to the hot water bath? Why or why not?

1. What quantities are needed to be measured in this Objective?
2. Which equation(s) will you use for this Objective?
3. How much water will you add to the calorimeter before the ice is inserted? Is more better than less?
4. When will you begin taking temperature measurements of the calorimeter bath?
5. How much ice will you use? Is more better than less? What factors enter into your decision?
6. How will you know when to stop taking data for this Objective?
7. How is determined for each material in this Objective?
8. What is the uncertainty of the measurements?

1. How did you determine the density of your metal?

These Questions are also found in the lab write-up template. They must be answered by each individual of the group. This is not a team activity. Each person should attach their own copy to the lab report just prior to handing in the lab to your TA.

1. Which is the better calorimeter: the traditional wooden one, or the styrofoam cup? Justify your reasoning.

2. Of the materials listed in Table 1, which is the best choice for storing solar heat energy captured by solar cells? Why?

3. What are the advantages of using styrofoam coffee cups over aluminum ones?

4. In Objective 2 we assumed that there was no heat lost to styrofoam calorimeter. Was this a valid assumption? Justify your conclusion.

5. Use the fact that (the specific heat of water) is large to help explain the role that oceans play on the world's climate.

6. Why are pots used for cooking often made of copper bottoms with aluminum sides? You may need to consider the metals' specific heats, densities and price per pound.

• Let the students know that if the string falls in the hot water bath that you, the TA, will remove it.
• Do not allow the vernier calipers become wet.
• When finished, the students should re-tie the temperature sensor cable. Do not misplace the twist ties.
• The vernier calipers, thermometers and temperature probes should be stored on the TA desk and returned at the end of each lab period.
• It may be enlightening for groups to present their temperature data during the oral presentations. It will give the other groups to point out obvious mistakes: beginning the data taking process too late; ending the data taking process too soon; touching the hot ingots with the temperature probe, etc.
• You may wish for students to analyze these two temperature screen shots for a quiz grade or part of an oral presentation. They should be able to discuss the mistakes made by the experimenters. Quiz #1 | Quiz #2

Vernier tutorial.