Calorimetry

Type of physical science: Chemistry

Field of study: Chemical methods

Calorimetry is the name given to a collection of experimental techniques whose aim is to measure energy changes and heat flows that accompany chemical reactions and physical changes. These experimental methods are the basis for determining the heating values of fuels, the energy content of foods, and the relative stabilities of related chemical substances.

Overview

"Calorimetry" is derived from two Greek words, calor, meaning "heat," and meter, meaning "measure." Loosely speaking, calorimetry is the collection of experimental methods aimed at measuring heat. A calorimeter is a device whose purpose is to measure heat flows, or energy that is liberated during physical or chemical changes. Most calorimeters have some general features in common. Heat flows, or energy changes, are measured only indirectly.

Temperature changes and the amount of energy dissipated in some sort of a heating element are what are normally measured. Mathematical relationships, along with the laws of thermodynamics, connect the measured quantities to the desired quantities.

Since there are many kinds of physical and chemical changes, there are many kinds of calorimeters. In order to illustrate the principles behind the operation of most of these, a specific example will be used, namely, the combustion, or "bomb" calorimeter.

The bomb calorimeter has two principal components. The first is the bomb, or reaction container. The second is the water-filled bucket into which the reaction container is placed. The reaction container is a stainless steel vessel having a volume of about 0.5 liter, with a lid that is screwed down tight enough to create an airtight seal. Inside the reaction container is placed a small cup capable of holding about 1 or 2 grams of the solid or liquid to be reacted. In the lid of the reaction vessel is a valve that allows a gas, usually oxygen, to be admitted into the vessel under moderate pressure. Also sealed into the lid are a pair of electrical connections, passing into the inside of the reaction vessel. On the underside of the lid, an ignition wire is connected to the electrical connections. When the lid is placed on the vessel, this ignition wire comes in contact with the chemical contained in the small cup. The sealed reaction vessel is suspended in the water bucket, now filled with water. In addition, a thermometer and a heating wire (different from the ignition wire in the reaction container) are placed in this water, along with a stirrer.

The calorimetric experiment is performed in the following way. The sample is weighed out in the small cup. The latter is suspended in the reaction container, which is then sealed. The entire assembly is suspended in the bucket of water, and the complete system is allowed to come to an equilibrium state such that the temperatures of the reaction vessel, its contents, and the water in the bucket become equal. The temperature of the water is recorded. Then an electrical current is passed through the electrical connections on the reaction vessel, which in turn passes through the ignition wire in contact with the chemical under study. In the atmosphere of pure oxygen, the chemical in the cup ignites at the point where it is in contact with the hot wire, and then it burns rapidly and completely. The energy that is liberated now raises the temperature of the reaction vessel and all that is in contact with it; namely, the water in the water bucket.

Throughout the process, the water in the bucket is stirred to allow temperature equilibration. The temperature of the system will rise and reach a constant level. Since most combustion reactions are rapid, the temperature rise is complete in a few minutes or less. The rise in temperature is noted. (Note that there are complications that need not be discussed for a complete understanding of the process. For example, accompanying the temperature rise resulting from the reaction, there will be a slow temperature drop as a result of the heat loss from the water bucket to the laboratory. This side effect, as well as several others, must be accounted for.) Then the heating coil in the water bucket is turned on, causing a second rise in temperature. By recording the amount of time that the current was passed through this second heating wire, the time that it was passed through the wire, and the resistance of the wire, the amount of electrical energy expended can be calculated. From the two temperature rises and the known electrical energy expenditure, the amount of energy liberated by the chemical reaction can be calculated. Since the mass of the chemical reacted is known, the amount of energy liberated for this chemical per unit amount of material, usually given in joules per kilogram, can be calculated.

The combustion calorimeter just described in some detail illustrates the principal features of all calorimeters. First, there must be a container for the materials undergoing the transformation. If gases and condensed materials are involved, as above, the container must be capable of being sealed tightly. If only condensed materials are involved, airtight seals are unneccessary. In the study of the combustion of gases, one replaces the sealed container with a flow tube, in which the gases are mixed. In this case, a flame becomes the object of study.

Second, there must be a device for measuring temperature changes. Calorimetry goes hand in hand with thermometry. Mercury-in-glass thermometers have been developed that allow the precise measurement of temperature changes of a few tenths of a degree. Semiconductor materials, called thermistors, have been developed with electrical properties that are very sensitive to temperature. A much older technology, in which thermocouples use simple devices consisting of two dissimilar metal wires in contact also allow the electrical monitoring of temperatures. A classical example of the thermocouple thermometry exists in which temperature changes of a few millionths of a degree were recorded. Third, there must be a device for calibrating the system. In the bomb calorimeter example, a heating coil was used to deliver a known amount of energy to the system. Such sources of energy can be calibrated very precisely, leading to very precise measurements of energy generation. In some calorimeters, it is more convenient to calibrate the instrument by first measuring temperature changes caused by reacting materials for which energy release has already been accurately measured, and then repeating the experiment with the unknown materials. Once again, some materials lend themselves to precise calibrations.

An interesting, large-scale calorimeter has been constructed using a properly insulated room in order to study the total energy changes accompanying the activities of a human subject.

In this case, temperature changes in the room resulting from the conversion of body fat and food into the work associated with muscular activity are measured, as well as the weight changes in the subject and the amounts of waste materials, including the water and carbon dioxide exhaled by the subject. In spite of appearances, the components of the bench-top laboratory calorimeter are present in this room calorimeter, and the mathematical framework needed to interpret the data is the same in both cases.

Applications

The numerical results of calorimetric experiments are used in various contexts. Perhaps the most familiar one is that of food values. Associated with foods is their calorie content. A donut is "worth" so many calories. These numerical values are obtained from the calorimetric experiment described above. In this case, a measured amount of foodstuff is burned, and the amount of energy liberated during the burning is obtained. (Actually, in many cases, the energy content of some food items is calculated from their composition in terms of fat, protein, and carbohydrate. Note also that the unit used for reporting the energy content of food is called the calorie but is, in fact, the "large calorie" or, more precisely, the kilocalorie. In addition, the accepted unit of energy is the joule, which is equal to 4.184 calories.) Now, the body performs work through muscular movement, but in performing work, the body is expending energy. It obtains this energy from the controlled "burning" of food. Because of the strict mathematical relationships between work and the energy content of food obtained from calorimetric experiments, weight reduction and maintenance programs are possible.

Calorimetry is valuable for determining the energy content of fuels. In particular, calorimetry is used to determine the amount of energy released when different fuels are burned in air. This allows the comparison of different types of fuels, such as gasoline, gasohol (a mixture of gasoline and ethanol, or grain alcohol), and methanol (wood alcohol). In this case, the energy released when a given number of grams of the fuel is burned is determined and then converted to the energy released per gallon. In this way, along with the cost per gallon, the relative cost of different fuels can be estimated. Data obtained from calorimetric experiments also allow the prediction of the efficiency of other fuels, including those used for the propulsion of rockets. For example, both liquid hydrogen and kerosene serve as fuels for different kinds of rocket engines.

Both fuels require oxygen for complete combustion; since rockets function in the airless environment of space, this oxygen, in a liquid form, must be transported with the fuel. It can be calculated using the data obtained from calorimetric experiments that the combustion of hydrogen generates more than twice as much energy as the combustion of an equal number of grams of kerosene, making it a more efficient fuel. (These calculations do not account for other factors, such as the difficulty in handling liquid hydrogen.)

The results of calorimetric experiments are used extensively by chemists. Because of the structure of the laws of thermodynamics, data obtained for chemical reactions by direct experiment can be combined to obtain data for chemical reactions that have not been studied by direct experiment. These laws are such that if the data for a reaction is obtained both by direct experiment and indirectly, the same numerical values (allowing for experimental uncertainties inherent in any experimental determination of a physical quantity) are obtained. Since many calorimetric experiments are time-consuming and require elaborate and expensive instrumentation, it is obviously beneficial to have the indirect route to data. Furthermore, the reaction for which data are desired often only occurs in the presence of other, interfering reactions, and so cannot be studied directly. The data obtained can be used, for example, to predict the stability of a chemical compound relative to different kinds of changes.

The calorimetric data can also be used in conjunction with experimental information of a different sort that gives information about the structure and shapes of molecules, and with theories that relate structure and shape to the calorimetric data. By means of these theories, the total energy of a molecule is, in a sense, divided up among the different units (chemical bonds) that make up the molecule. Different molecules are made up of different combinations of these units. It is found that, to a good approximation, when the same unit appears in different molecules, and when the energy of each of these molecules is distributed into the constituent units, a given unit ends up with the same energy, no matter what molecule that unit finds itself in.

(Clearly, the actual situation is somewhat more complex; however, the modifications introduced by the theory do not destroy the simplicity of the picture.) With the aid of computer programs, one can construct new molecules that have never been synthesized before out of the list of constituent units. Using the energy per unit obtained from the distribution of the calorimetric data from known molecules, one can calculate energies and, therefore, stabilities of new and unstudied molecules, often allowing decisions about whether the synthesis of such a chemical species is even possible. It is also possible to predict the detailed structure of known molecules from these calculations. This is often useful, since the experiments needed to determine structure are often difficult, time-consuming, and expensive. Furthermore, the structures (shapes) are often needed in determining, for example, the extent to which a new drug molecule will attach itself to the location on a cell where its therapeutic activities will be manifested.

Context

The first recorded use of a calorimeter is attributed to Joseph Black, in 1760. From that time on, calorimeters were employed for various practical purposes, but two questions arose early. First, What is heat? Initially, heat was assumed to be a substance and was given the name "caloric." It was hypothesized that this substance flowed between objects at different temperatures. A new wave of experimentation aimed at identifying the nature of heat became possible as the art of thermometry matured, allowing for the construction of the first calorimeters. The key experiment (a somewhat simplified view) was the calorimetric experiment performed by Benjamin Thompson as reported in his paper in 1798. It was a common experience that temperatures rose during the boring of cannons. This rise in temperature was ascribed to the freeing of the substance heat through the creation of the chips of metal. Thompson observed that the temperature continued to rise even after the drill had become blunted and ceased to produce chips. To test the hypothesis that given amounts of solid metal and metal chips do not contain different amounts of heat, he heated equal masses of a solid block of metal and metal chips to the same temperature and immersed each of them in equal masses of water initially at the same (lower) temperature. He observed that when the water and metal came to a constant temperature, there was no difference between the experiment involving the solid block of metal and the chips.

The system of water and thermometers was the "mixture" calorimeter. As experiments were multiplied, it became clear that no such substance existed. Although one talks of heat as if it were a substance, it really is an abstract mathematical quantity that measures the extent to which the process "heat flow" occurs.

The second key question centered around the concept of energy. Once again, energy turned out to be an abstract mathematical quantity that could be associated with matter and that measured the amount of work that could be done by that matter. It was observed at the beginning that energy could be converted from one form to another, but it was not clear whether energy could be created where it did not exist before. This question was of practical importance, because if energy could be created, then perpetual motion machines (devices that, once started, would continue to operate without external intervention) would be possible. Classical calorimetric experiments were performed by James Prescott Joule in which a falling weight was constrained to turn a paddle suspended in water. The falling weight caused a rise in temperature. Although the initial experiments were rather crude (the calorimeter was ill-suited for measuring small temperature differences), the results were consistent with what is now known as the mechanical equivalent of heat. As experiments were multiplied and calorimeters improved, it was found that energy was converted from one form to another with the total amount of energy involved remaining constant. This is the law of conservation of energy. Energy cannot be created or destroyed, but merely changed from one form to another.

From elaborations on the nature of heat and the discovery of the law of conservation of energy (the first law of thermodynamics), the entire science of thermodynamics was born. In a real sense, calorimetry has been an important tool for defining the very nature of modern science.

Principal terms

CHEMICAL REACTION: a process in which one or more chemical substances are converted into different substances

COMBUSTION: a specific type of chemical reaction in which a substance reacts with oxygen to form oxides, and in which large amounts of energy are usually released

ENERGY: a property of a mechanical system, or of a collection of reacting substances, that is a measure of the system's or substances' ability to perform work

HEAT: an imaginary fluid that is said to flow when two bodies of different temperatures are brought into contact with each other, resulting in equalization of their temperatures

TEMPERATURE: a property of all bodies that measures their "hotness" or "coldness" in terms of a numerical scale

WORK: an energy-consuming process that is solely mechanical in nature, and that is defined in terms of forces exerted and the distances over which these forces are exerted

Bibliography

Conant, James Bryant. HARVARD CASE HISTORIES IN EXPERIMENTAL SCIENCE. Cambridge, Mass.: Harvard University Press, 1957. A lengthy chapter in the first volume of this two-volume series gives an account of thermometry and heat that is very readable to the nonscientist. The Harvard Case Histories series, while dated, represents an excellent attempt to place the important advances in science in a historical context.

Hemminger, W., and Guenther Hohne. CALORIMETRY: FUNDAMENTALS AND PRACTICE. Translated by Y. Goldman. Deerfield Beach, Fla.: Verlag, 1984. This book is written primarily for the chemist. It contains many examples of different kinds of calorimeters, however. There is some historical matter distributed through the technical narrative. Contains useful diagrams that describe the basic kinds of calorimeters without overwhelming the reader with technical details.

Ihde, Aaron J. THE DEVELOPMENT OF MODERN CHEMISTRY. New York: Dover, 1964. This is a rather extensive history of chemistry that contains some information about the development of thermodynamics along with calorimetry. Valuable for placing the topic in the broader context of chemical science. There is biographical material about principal actors in the growth of modern chemistry.

Jaki, Stanley L. THE RELEVANCE OF PHYSICS. Chicago: University of Chicago Press, 1966. A rather scholarly but readable discussion of the growth of modern science as a mathematicized reading of nature. It starts off with the Aristotelian view of nature as an organism and works its way through mechanisms to mathematics. Recommended for the general reader who wants a philosophical history of science without being buried under philosophical jargon.

McCullough, John P., and Donald W. Scott. EXPERIMENTAL THERMODYNAMICS. New York: Plenum Press, 1968. This book is for professional chemists. Nevertheless, it is filled with detailed diagrams describing calorimeters as they are really used. These diagrams alone are valuable as pictorial demonstrations of the extent to which the art has been developed. Since the book is somewhat old, it does not describe the use of computers to control experiments, a very minor shortcoming.

McGlashan, M. L. CHEMICAL THERMODYNAMICS. New York: Academic Press, 1979. Rather technical, but the early chapters describe several types of calorimeters.

Laws of Thermodynamics