Warming Up!

Type

Physical Science

Grade

8th grade

Difficulty

Medium - Hard

Cost

Approximately $40

Safety Issues

• There will be electricity used so an adult will be on hand to supervise at all times
• The stovetop will be very hot so tongs will be used to set the pans with the test materials down on the stove while wearing heat resistant gloves and clothing. An adult will be on hand to supervise and assist.
• The test materials will be very hot even after initial heating so heat-resistant gloves and clothing will be worn while taking readings. An adult will be on hand to supervise and assist.
• The liquid test materials will boil and may sputter so goggles, heat resistant gloves, and heat-resistant clothing will be worn while interacting with the test materials. An adult will be on hand to supervise and assist.
• Flammable objects may ignite if hot materials are placed near or on them so all flammable objects will be removed from the vicinity of the experiment. A smoke detector has been checked and is operational. An adult will be on hand to supervise and assist.

Objective

The purpose of this experiment is to determine whether a correlation between heat capacity and heat retention is present and to identify a material that would have the highest of both qualities if it was to be used as a warmer.

Materials

For this experiment, one would need the following materials, at a grocery or department store. For the sand and stone, it is advisable to visit a park or beach to find them. All of the materials are readily available.

• 200 grams of water
• 200 grams of vegetable / cooking oil
• 50 grams of salt
• 50 grams of sand
• 50 grams of baking soda
• 50 grams of small gravel
• A stone weighing approximately 50 grams
• 2 tablespoons of black ink or food coloring
• 7 muffin tins - Electric range
• Infrared Thermometer
• Safety goggles
• Heat resistant gloves and clothing
• Kitchen scale capable of measuring small quantities
• 1 timer
• 1 stopwatch
• Permanent Marker
• 18 labels
• 1 hot plate stand
• Tongs

Introduction

I got the idea from this experiment while I was in Russia one winter. My greatgrandmother lives in a small village where there is no central heating. She cannot use the fireplace overnight because if she opens the chimney shutter, all of the heat will escape through the top. She can't close the shutter because then she would risk suffocation as the smoke would stay inside the house along with the heat. I suggested heating up a big rock like I saw in saunas. That was when I began to wonder if there was a corellation between heat capacity (the amount of time / energy needed to heat an object) and heat retention (the amount of time an object stays hot after you remove the heating source). I also began to wonder which material would be the best to use as an overnight warmer for my great-grandmother.

Terms & Concepts for Background Research

Heat is a transfer of disordered energy at the molecular level. Heat is created by the movement of atoms and molecules present in all matter.The Joule, which is expressed in written notation as J, is used to measure the mechanical equivalent of heat. The Kelvin is the unit of measurement for the thermodynamic (absolute) temperature scale. The scale starts at absolute zero, the theoretical lowest temperature matter can be at where there will be a complete absence of heat which is approximately -273°C. Heat capacity can be described as the heat energy needed to raise the temperature of one unit of a substance by one unit of temperature. Heat retention is the measure of how long an object stays warm after it is heated. It could be expressed as the time it takes an object to cool to a certain point.

Research Questions

• Is there a relationship between heat capacity and heat retention? What is it?
• Which material has the highest heat capacity?
• Which material has the best heat retention qualities?
• Which of the materials would be the most practical for use as a warmer?

Experimental Procedure

Preparation

1. Measure and record the average temperature in the room with the infrared ! thermometer. This can be done by taking the temperatures of several walls and finding the average
2. Measure out 50 grams of each test material
   1. Weigh the material in the muffin tin
   2. Subtract the weight of the muffin tin from the total weight and add or remove material as necessary
3. Pour the ink / food coloring, one tablespoon each, over the white materials: salt and baking soda. Try to get an even spread around the center. The ink will enable a more precise measurement with the infrared thermometer as it has trouble with measuring white or metallic surfaces.
4. Label each tin cup, stopwatch and timer with the same corresponding letter for each test material
   1. "A" for the water
   2. "B" for the baking soda
   3. "C" for the vegetable/cooking oil
   4. "D" for the sand
   5. "E" for the small gravel
   6. "F" for the salt
   7. "G" for the stone
5. Make sure to put on protective clothing, gloves, and goggles before beginning the experiment.

Part 1: Determining Specific Heat Capacity

1. Specific Heat Capacity can be expressed as:

C = Q * time / amount of substance / ΔT !

(Referred to as Formula 1) where C is the heat capacity, Q is the heat energy ! transferred to the item, and ΔT is Tf - Ti, where Tf is the final temperature and Ti is the initial temperature.

2. DetermineQ: Q is the amount of heat energy transferred to the item. It is ! expressed in Joules (Joules=watts per second). Because the heat capacity of water is known (4.18 Joules/gram), Q can be determined by taking the temperature of 50 grams of water, heating it for 10 seconds, recording the temperature after, finding the temperature difference (ΔT), and inserting all these parts into Formula 1 along with the known heat capacity of water. The equation should then look like: 4.18 = Q * 10s / 50g / ΔT  The Q calculated as a result of this equation will be used to compute the heat capacity of all of the other materials as Q is affected by the range, not the type of material being heated.
3. Determine time, amount of substance, and ΔT: To do this, take the test item, and, as it weighs 50g, the amount of substance is 50. Record its temperature. Then, heat it for 10 seconds in the muffin tin and immediately record its temperature again. The time is 10 seconds. Finally, ΔT is Tf - Ti, or the difference between the final and starting temperatures.
4. Calculate Heat Capacity: Now put the parts found in steps 2 and 3 into ! Formula 1. It should look like: C = Q (found in step 3) * 10 (time, step 3) / 50 (grams, step 3) / ΔT (Tf - Ti, step 3)
5. Repeat steps 3 and 4 for each of the other materials. The terms for Q, time, and amount of substance are constant for each item.

Part 2: Determining Heat Retention Qualities

1. Add 50 g of each material to each muffin tin (Preparation: step 2)
2. Turn the electric range on to maximum
3. Place tin candleholder "A" on the range using the tongs and start the stopwatch
4. Take readings with the infrared (IR) thermometer every 30 seconds until the test material reaches a temperature of 70° Celsius
5. Immediately stop the stopwatch and take the muffin tin off the range using the tongs. Put it on the hot plate stand
6. Reset the stopwatch, then start it
7. Take a reading after thirty seconds:
   1. Take and record three readings with the IR thermometer
   2. Find the average
   3. Record any observations related to the test material
8. Repeat Step 7 for 5 minutes
9. Now take readings every minute until the stopwatch hits 10 minutes (see steps 7a and 7b to find out how)
10. Take a final reading at 15 minutes (see steps 7a and 7b to find out how)
11. Record any observations related to the test material
12. Repeat steps 3-9 for the materials labeled "B", "C", "D", "E", "F", and "G"
13. Record any other observations !

Results

Observations Made During the Experiment

Throughout the experiment, several interesting occurrences were observed:

• Initially, the experiment did not include calculating the efficiency of the range. However, during the experiment, the numbers weren't matching up (checked against the known heat capacity of water) so it was decided to calculate the efficiency. Startlingly, only 97.99 watts of the range's 1500 watts were going towards heating the samples. This can be explained by the fact that the muffin tin covered only a small part of the burner and that most of the heat given off by the range diluted into the surrounding air.
• The thermometer showed erratic temperatures at times. It was decided to take ! multiple readings each time, getting rid of the outliers and then calculating the arithmetic mean.
• When temperatures were measured first of the materials and then of the tins they were in, drastically different readings were obtained. Upon further research this was attributed to the IR thermometer's inability to read metallic surfaces.
• The ink, which was added to increase the accuracy of the IR thermometer with ! white substances, clotted and solidified as soon as it got heated, forming a sort of caking over the baking soda and salt. Solidification at high temperatures is a known property of ink.
• The tins started to shake when heated and needed to be held with tongs at all times. This was most likely caused by three things: the tins had uneven bottoms, molecular movement increased with rising temperatures, and the liquids bubbled slightly as they got closer to their boiling points.
• Some materials' (stone, small gravel, sand, and salt) temperatures kept rising even after they were removed from the heat source - at first this was attributed to the thermometer's failure but it showed up on several occasions, even after the batteries in the thermometer were changed.

Numerical Data

The experiment had four main parts: determining heat capacity, determining heat ! retention qualities, seeing how the first affects the second (discussed in ! conclusion), and finally looking at the practicality of using a particular material as a warmer.

Heat Capacity

The first part of the experiment was determining the specific heat capacity of the test samples. These capacities are expressed in the data table and graph shown below:

From this graph, one can see that the baking soda had the highest heat capacity of 6.46 Joules per gram, the stone coming in a close second at 6.33 Joules per gram. Salt had the lowest heat capacity at 2.64 Joules per gram and small gravel second worst at 3.47 Joules per gram. Therefore, it would take the least amount of energy to heat salt and the most amount of energy to heat baking soda.

Heat Retention Qualities

The second part of the experiment was seeing how a heated object retained its warmth. The following graph shows the test materials' temperature changes over a period of 15 minutes.

The graph shows that at the end of the 15 minute experiment, the stone was still the hottest at a temperature of 315.15 Kelvins while the salt was the coldest at 303.15 Kelvins. The other items' temperatures were (ordered highest to lowest): Sand - 312.8 Kelvins, Oil - 311.3 Kelvins, Small Gravel - 308.4 Kelvins Water - 307.8, and Baking Soda - 307.8 Kelvins. The Salt, Stone, Sand, and Small Gravel continued to heat up, even after they were removed from the heat source. The oil and water followed their trend lines the most while the small gravel had the most abrupt heat loss.

This graph, however, does not give us a full measure of heat retention because it reflects an improper definition of heat retention.

Defining Heat Retention:

The question of how to measure heat retention rose several times throughout the experiment. Because there are no formal units or formulas used to define heat retention, it was necessary to create a case- specific definition for heat retention.

#1) the temperature drop One of the ways to measure heat retention that were considered was to take the difference between the initial temperature and the final temperature. This would give one a numeric representation of how much heat a material lost during the experiment. This type of measurement would be good if one only cared about the end result such as if one was cooking dinner and needed the food to be a certain temperature after 15 minutes. However, if one was to be using a material as a warmer, one would care about the temperature during the experiment, and not after it. For this reason, this measurement could not be used to measure heat retention.

#2) the temperature's arithmetic mean The second plausible way to measure heat retention is to take the arithmetic mean of all of the temperature measurements. This way is better than the other two because it would reflect any rises or drops in temperature. However, the fault with this way is that it would not show the difference between a set of temperatures, for example, that could be 10, 8, and 0 (a drop at the end) and 6, 6, and 6 (a consistently low temperature). For that reason, the mean couldn't be used to calculate heat retention for the purpose of this experiment.

#3) the temperature function's integral The final way to measure heat retention, the one chosen to be used in this experiment, is to take each material's function integral. Simply speaking, an integral is the area between a function's line and the x- axis. In general, calculating the integral of a function involves complex calculations, but in this experiment's, it is only necessary to find the area of each trapezoid formed by the part of the material's function between point A and point B, the distance on the x-axis, and the lengths of two perpendiculars from points A and B to the x-axis. One would then add all of the trapezoid's areas to find the integral for the whole function. This measurement would be the most accurate because it not only takes into account temperature for all of the points on each function but also shows the changes in temperature throughout the experiment

To give a more accurate measure of each material's heat retention qualities, the integral of each material's graph was calculated. Those results are reflected in the graph below.

From this graph, one can see that the sand had the best heat retention (although its end temperature was only the second highest). However, it would be the best to use as a warmer because it had a higher temperature throughout the experiment, even though the temperature dropped at the end.

Connecting the Dots

While the previous graphs allow for comparison of the heat capacities and retention qualities of the materials against each other, they never show the two together. The graph on the next page is a scatter plot where the x-axis reflects heat retention in Kelvins*seconds and the y-axis reflects heat capacity in Joules per Gram.

To find out if this graph supports the hypothesis of a higher heat capacity meaning better heat retention and vice versa, one can look at the point farthest on the left; it should also be the lowest on the graph. In general, a point should be proportionally as far on the x-axis as it is on the y-axis. For example, if a point is halfway up the y-axis, it should be halfway on the x-axis, and so on.

Having done this check, it becomes evident that the majority of the materials support the hypothesis (5 out of 7) The only outliers are the baking soda and the small gravel, but it can be predicted that in a larger scale experiment, approximately 70% of the materials tested will support this experiment's hypothesis.

Practicality While some items may retain heat for long periods of time, a good warmer needs to be practical and have the ability to be heated quickly and efficiently. The graph below shows the heating rates of the test materials.

Conclusion

The Hypothesis

The original experiment question was to see whether a high heat capacity meant good heat retention, therefore making a particular material a good candidate for use as a body warmer. My hypothesis was that a higher heat capacity would mean better heat retention and that a stone would have the highest heat capacity. The results of this experiment supported the hypothesis in multiple ways. Most of the materials' results showed that a higher heat capacity does mean better heat retention. Even though the stone did not have the highest heat capacity, it came in second place in the heat capacity test and had the 3rd highest heat retention. Baking soda, which had the highest heat capacity, had one of the lowest results for heat retention. However, it is reasoned that this still doesn't counter the hypothesis because the baking soda results could have been incorrect: the baking soda was white and white substances have a greater potential for error with the IR thermometer. The erratic timeline for the baking soda's retention results support this explanation. Overall, while the data from this experiment generally support the hypothesis, more materials would need to be tested to have conclusive results.

The Results

Heat Capacity

Most of the results in the heat capacity portion of the experiment were as expected. Most of the solids used in the experiment demonstrated a higher heat capacity than the liquids and it is expected that this will show again if further testing is conducted. However, the experiment also gave several unexpected results. For one, the baking soda had the highest heat capacity exceeding even that of the stone. This is most likely because it was packed tightly in the tin, making it almost like the stone. Also, the salt had the lowest heat capacity when, being a solid, it was expected to have one of the higher heat capacities. As mentioned above, however, both of these materials are white in color, possibly affecting their results. Ink was used to darken the materials and make results more accurate but even having done that, the potential for error is higher than that of the other materials.

Heat Retention

As expected, there is definitely a connection between a material's heat capacity and its heat retention qualities. Based on the small sample used in this experiment, one can conclude that a higher heat capacity would mean better heat retention. There were also several other interesting results in the experiment. For one, while they were very close, the liquids had a higher average drop in temperature over 30 seconds. Another interesting fact is that the salt, stone, small gravel, and sand all continued to get hotter even after they were removed from the heat source, as seen in the heat retention temperature graph. The same graph also shows that these items then went on to have generally steeper temperature declines than those whose temperature did not increase post-heating. An interesting fact is that the sand and small gravel both had temperature declines after the tenth minute that were much sharper than those of the other materials.

Practicality and Use as a Warmer

The real-life side of this experiment was the possibility of using the natural test materials as warmers instead of commercial, chemical products. To look into the practicality of such use, a graph (see in results) was created showing the heating speeds of the materials. This is important because most commercial warmers act instantaneously or need to be heated for just a few minutes. The graph shows that most of the items with high heat capacities and good heat retention qualities take longer to initially heat. While all of the samples reached the target temperature of 70°C or 343.15 Kelvins within 2 minutes, 45 seconds, the samples were only 50 grams each, not even enough to fully fill a muffin tin. While a larger amount of material would have better heat retention qualities, it would have to be heated for longer amounts of time and be bulky, particularly with the stone, making it impractical as a warmer. If a user is unconcerned about size, however, larger amounts of material could be used for a warmer if it wouldn't be movable such as one for use overnight. Overall, while the samples do have the theoretical potential to be used as warmers, none of them are small or practical enough to allow them to be compared to commercial warmers.

Explaining the Results

Density offers an explanation for the heat capacity results. The table below shows the densities of the test materials used. Salt can be excluded because of the potential for error with the infrared thermometer. Then, with the exception of the small gravel and water, the materials show that a higher density means a higher heat capacity. The heat retention qualities of the gravel can be explained by the way the loose rocks had gaps in them, allowing airflow and cooling on all sides rather than just the top as with the other liquids. Another possible scientific explanation for the heat capacities of materials is their molecular arrangement. Heat capacity is the measure of how much energy is needed to raise the temperature of a substance by 1 Kelvin and heat is caused by vibrations in the atoms and molecules of a substance. Therefore, heat capacity can be expressed as the energy needed to cause these molecules and atoms to move and vibrate faster. In a solid, the molecular arrangement is usually tighter, with more bonds between the molecules. Because of this, it can be reasoned that it would be harder to move the molecules of a solid, meaning it would need more energy to raise its temperature (a higher heat capacity). In liquids, where the molecular arrangement is more loose and random, there are less bonds between the molecules, meaning it would take less energy to move them, hence a lower heat capacity.

Further Research

Improvements

There were several things that could have been done to improve the experiment. One limitation was the amount of samples that was tested; more samples would have allowed for a more conclusive verdict. A potential source of error in the experiment was the infrared thermometer. The batteries ran out and were replaced during the experiment, which may have affected the results. A more expensive thermometer would have most likely offered more precise readings. If this experiment was repeated, more measures would be taken to overcome the white color problems. Another piece of more expensive equipment that could have been used is a calorimeter, which could have given more accurate results.

Follow-up Questions

The data from this experiment gave rise to many new research questions that can lead to follow-up experiments. One of these would be to see if or how density affects heat capacity. In the experiment, the denser items such as the stone and baking powder had higher heat capacities than less dense items such as the loose gravel or the water. Another question that comes up relates to why some of the items continued to heat up after they were removed from the heat source. This is particularly interesting because it happened with only some of the test samples.

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