HEAT TRANSFER AND COMPARATIVE HEAT CAPACITIES

HEAT TRANSFER AND COMPARATIVE HEAT CAPACITIES

Knight Foundation Summer Institute

Terry Newirth, Haverford College

Introduction:

This is similar to the first two experiments in this section, but here the heat content of two common metals used for cooking utensils, aluminum and copper, are compared to the heat content of water. Again we measure the heat transferred from hot material to room temperature water to provide the data. The data analysis can be done very simply to provide the relative heat content, or with a slightly more sophisticated data analysis, fairly good numbers for the actual heat capacities of the metals can be determined.

There are many ways that this has direct relevance to Technology and Metals Aluminum and copper are both common metals used in the pots and pans we use to cook. We see that the heat capacity of copper is very low. That means that relatively little heat is needed to raise the temperature of copper, i.e. it heats up very fast. That is why some pots have copper bottoms, it helps to heat the pot up more quickly and evenly. Aluminum pans heat up a little more slowly, but retain more heat. Water heats up much more slowly than either metal, but retains much more heat.

Modern technology uses the large amount of heat that can be transferred from water as a source of energy, e.g. in heat pumps. Geothermal energy also relies on heat transfer. In that case air or water on the earth's surface exchanges heat with cold deep ocean waters of cool deep earth. (http://www.ghpc.org) This site shows how heat pumps work and lists some schools that use heat pumps for energy.

Objectives:

To have the students determine the heat capacity of aluminum, copper and water

To understand how the varying heat capacities effects the uses and properties of different substances

Vocabulary:

Heat Capacity

Heat Transfer

Heat Lost

Heat Gained

Materials:

1 hot plate/ class

Balance/class

1 beaker, at least 150 ml for boiling water/class

1 150 ml beaker for stabilizing Styrofoam cups

2 Styrofoam/group

25 ml graduated cylinder

Thermometer

Water

Copper wire

Steel washers

String

Procedure:

Fill the beaker about 3/4 with water and bring to a boil on the hot plate.

Using the graduated cylinder, measure 50 ml of water into two stacked Styrofoam cups, which are placed in a 150 ml beaker for extra stability.

Place the thermometer in the cups.

Weigh the copper wire or aluminum sample on the balance and record the weight in the lab book.

Tie about a foot length of string onto the metal sample and suspend the metal sample in the boiling water in such a way that it can be pulled out by the string.

Record the temperature of the water in the Styrofoam cup in the lab book.

After the metal sample has been in the boiling water for a few minutes, quickly pull it out and place it in the Styrofoam cup. Stir gently with the thermometer and record the highest temperature the solution reaches.

Repeat steps 2 - 7 with the other metal if desired.

Repeat 2, 3, and 6. Then pour some boiling water into the graduated cylinder (at least 5 ml). Quickly record the volume of the boiling water and pour it into the Styrofoam cup. Stir gently with the thermometer and record the highest temperature the solution reaches.

Calculations:

a. Simple Method

One can get determine the relative heat content of copper, aluminum and water, by simply comparing the temperature rise of the 50 ml of water in the Styrofoam cup/g of material added. For water assume a density of 1 g/ml, so ml's = 8's. The greater the temperature rise of the water/g of sample, the greater the heat content of sample, i.e. it had more heat to transfer to the water to heat it.

b. More Advanced Method

This method involves more calculations and can be used to demonstrate, or reinforce the method of dimensional analysis. It is based on one of the most fundamental principles of science: the conservation of energy. In this context that means that all the heat that left the hot object was transferred to the cold water or

heat lost = heat gained

The heat capacity of pure water is 1 cal/g ¡C, which means that it takes one cal of heat to raise the temperature of one gram of water one degree Centigrade. For this experiment, even though we are using tap water, we will assume that our water also has a heat capacity of 1 cal/g ¡C, and a density of 1 g/ml. Since we know we started with 50 ml of water and we know how many degree the temperature of this water was raised, we can calculate how much heat, in cal, was transferred to the water. E.g. Let's say that when we put 5.4 grams of 100¡C aluminum in our water (aluminum that had been suspended in boiling water) the temperature of the 50 ml of water was raised from 26.0¡C to 27.8¡C. Since the density of water is 1 g/ml, 50 ml of water has a mass of 50 g. Therefore our calculation of the heat transferred to the water would be:

1cal/g/^oC x 50g water x 1.8^oC = 90cal = heat gained by water = heat lost by aluminum

Notice in dimensional analysis, units in the fractions get canceled, just like numbers do in fractions. Here we had gram in the numerator and denominator, as well as ¡C in the numerator and denominator, so they both cancel and the units of the answer are only in cal. In science calculations units are VERY important. All numbers should have units after them.

Now we know how much heat was transferred to the water. The heat obviously came from the hot material we added to the water. Heat capacity is the heat lost (or gained) per g material per ¡C. Since we know the grams of the metal we added, the change in temperature of the metal we added (100¡C – final temperature of the water in the cup) and the heat transferred from that material we can calculate the heat capacity of the metal. For the example above we just plug the numbers we know into the definition of heat capacity. We had 5.4 g of Aluminum, which transferred 90 cal of heat (calculation above) and the aluminum cooled from 100¡C to 27.8¡C, or 72.2¡C. Therefore the heat capacity of aluminum is

We have made some assumptions that aren't entirely correct, e.g. we used tap water and not pure water. We also did not use a very accurate thermometer to measure the temperature change or the volumes of water. We also assumed that no heat was transferred to the Styrofoam cup or to the air in the transfer process. Nonetheless the answers one gets from these calculations are good enough to see that the heat capacity of copper<aluminum<<<water.

Assessments:

The students could hand in a lab report with all of the data that they collected as well as their interpretations of the data.

Extensions:

Below are a list of topics that could be used in discussion with the entire class.

Water can absorb a relatively large amount of hear (energy) before its temperature rises. When it cools, it releases a relatively large amount of energy. As the solvent of our bodies, that means, that even on a very hot day, our body temperature does not get too hot. The heat is stored in the water (blood) and released as the body cools. When it is cold outside, our body water will cool slightly and release a large amount of heat to warm us up. This is one of the mechanisms that our bodies use to maintain relatively constant body temperature.

Related to heat capacity is water's high heat of evaporation. When we are hot, our body responds by sweating. It takes a lot of heat to make water (sweat) evaporate, and that heat comes from our body, making us cooler.

Philadelphia Science Content Standards:

SCIENCE CONTENT STANDARD # 1: NATURE OF SCIENCE

This content allows the students to "design, modify and conduct an investigation through testing, revising, and occasionally discarding idea, all of which lead to a better understanding of how things work." Also, as benchmark number 2 states, the students will learn to "collect and summarize data from an experiment and interpret results in terms of the data."

Cross References:

The students are using analytic skills as well as mathematical skills in the computation of their results. In the extensions, the students are using Language Arts skills to write about the topics provided.