Warming Up! (page 2)

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Author: Anton U.


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


  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.

  1. 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.
  2. 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.
  3. 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)
  4. 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 !


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.


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