Coffee Cup Calorimeter Lab Conclusion Essay

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Specific Heat

Specific heat is the amount of heat that must be added to, or removed from, a unit of mass for a given substance to change its temperature by 1°C. Thus, a kilocalorie, because it measures the amount of heat necessary to effect that change precisely for a kilogram of water, is identical to the specific heat for that particular substance in that particular unit of mass.

The higher the specific heat, the more resistant the substance is to changes in temperature. Many metals, in fact, have a low specific heat, making them easy to heat up and cool down. This contributes to the tendency of metals to expand when heated (a phenomenon also discussed in the Thermal Expansion essay), and, thus, to their malleability.


The specific heat of any object is a function of its mass, its composition, and the desired change in temperature. The values of the initial and final temperature are not important—only the difference between them, which is the temperature change.

The components of specific heat are related to one another in the formula Q = mc δ T. Here Q is the quantity of heat, measured in joules, which must be added. The mass of the object is designated by m, and the specific heat of the particular substance in question is represented with c. The Greek letter delta (δ) designates change, and δ T stands for "change in temperature."

Specific heat is measured in units of J/kg · °C (joules per kilogram-degree Centigrade), though for the sake of convenience, this is usually rendered in terms of kilojoules (kJ), or 1,000 joules—that is, kJ/kg · °C. The specific heat of water is easily derived from the value of a kilo-calorie: it is 4.185, the same number of joules required to equal a kilocalorie.


The measurement of heat gain or loss as a result of physical or chemical change is called calorimetry (pronounced kal-IM-uh-tree). Like the word "calorie," the term is derived from a Latin root meaning "heat."

The foundations of calorimetry go back to the mid-nineteenth century, but the field owes much to scientists' work that took place over a period of about 75 years prior to that time. In 1780, French chemist Antoine Lavoisier (1743-1794) and French astronomer and mathematician Pierre Simon Laplace (1749-1827) had used a rudimentary ice calorimeter for measuring the heats in formations of compounds. Around the same time, Scottish chemist Joseph Black (1728-1799) became the first scientist to make a clear distinction between heat and temperature.

By the mid-1800s, a number of thinkers had come to the realization that—contrary to prevailing theories of the day—heat was a form of energy, not a type of material substance. Among these were American-British physicist Benjamin Thompson, Count Rumford (1753-1814) and English chemist James Joule (1818-1889)—for whom, of course, the joule is named.

Calorimetry as a scientific field of study actually had its beginnings with the work of French chemist Pierre-Eugene Marcelin Berthelot (1827-1907). During the mid-1860s, Berthelot became intrigued with the idea of measuring heat, and by 1880, he had constructed the first real calorimeter.


Essential to calorimetry is the calorimeter, which can be any device for accurately measuring the temperature of a substance before and after a change occurs. A calorimeter can be as simple as a styrofoam cup. Its quality as an insulator, which makes styrofoam ideal for holding in the warmth of coffee and protecting the hand from scalding as well, also makes styrofoam an excellent material for calorimetric testing. With a styrofoam calorimeter, the temperature of the substance inside the cup is measured, a reaction is allowed to take place, and afterward, the temperature is measured a second time.

The most common type of calorimeter used is the bomb calorimeter, designed to measure the heat of combustion. Typically, a bomb calorimeter consists of a large container filled with water, into which is placed a smaller container, the combustion crucible. The crucible is made of metal, having thick walls with an opening through which oxygen can be introduced. In addition, the combustion crucible is designed to be connected to a source of electricity.

In conducting a calorimetric test using a bomb calorimeter, the substance or object to be studied is placed inside the combustion crucible and ignited. The resulting reaction usually occurs so quickly that it resembles the explosion of a bomb—hence, the name "bomb calorimeter." Once the "bomb" goes off, the resulting transfer of heat creates a temperature change in the water, which can be readily gauged with a thermometer.

To study heat changes at temperatures higher than the boiling point of water (212°F or 100°C), physicists use substances with higher boiling points. For experiments involving extremely large temperature ranges, an aneroid (without liquid) calorimeter may be used. In this case, the lining of the combustion crucible must be of a metal, such as copper, with a high coefficient or factor of thermal conductivity.

Heat Engines

The bomb calorimeter that Berthelot designed in 1880 measured the caloric value of fuels, and was applied to determining the thermal efficiency of a heat engine. A heat engine is a machine that absorbs heat at a high temperature, performs mechanical work, and as a result, gives off heat at a lower temperature.

The desire to create efficient heat engines spurred scientists to a greater understanding of thermodynamics, and this resulted in the laws of thermodynamics, discussed at the conclusion of this essay. Their efforts were intimately connected with one of the greatest heat engines ever created, a machine that literally powered the industrialized world during the nineteenth century: the steam engine.


Like all heat engines (except reverse heat engines such as the refrigerator, discussed below), a steam engine pulls heat from a high-temperature reservoir to a low-temperature reservoir, and in the process, work is accomplished. The hot steam from the high-temperature reservoir makes possible the accomplishment of work, and when the energy is extracted from the steam, the steam condenses in the low-temperature reservoir, becoming relatively cool water.

A steam engine is an external-combustion engine, as opposed to the internal-combustion engine that took its place at the forefront of industrial technology at the beginning of the twentieth century. Unlike an internal-combustion engine, a steam engine burns its fuel outside the engine. That fuel may be simply firewood, which is used to heat water and create steam. The thermal energy of the steam is then used to power a piston moving inside a cylinder, thus, converting thermal energy to mechanical energy for purposes such as moving a train.


As with a number of advanced concepts in science and technology, the historical roots of the steam engine can be traced to the Greeks, who—just as they did with ideas such as the atom or the Sun-centered model of the universe—thought about it, but failed to develop it. The great inventor Hero of Alexandria (c. 65-125) actually created several steam-powered devices, but he perceived these as mere novelties, hardly worthy of scientific attention. Though Europeans adopted water power, as, for instance, in waterwheels, during the late ancient and medieval periods, further progress in steam power did not occur for some 1,500 years.

Following the work of French physicist Denis Papin (1647-1712), who invented the pressure cooker and conducted the first experiments with the use of steam to move a piston, English engineer Thomas Savery (c. 1650-1715) built the first steam engine. Savery had abandoned the use of the piston in his machine, but another English engineer, Thomas Newcomen (1663-1729), reintroduced the piston for his own steam-engine design.

Then in 1763, a young Scottish engineer named James Watt (1736-1819) was repairing a Newcomen engine and became convinced he could build a more efficient model. His steam engine, introduced in 1769, kept the heating and cooling processes separate, eliminating the need for the engine to pause in order to reheat. These and other innovations that followed—including the introduction of a high-pressure steam engine by English inventor Richard Trevithick (1771-1833)—transformed the world.


The men who developed the steam engine were mostly practical-minded figures who wanted only to build a better machine; they were not particularly concerned with the theoretical explanation for its workings. Then in 1824, a French physicist and engineer by the name of Sadi Carnot (1796-1832) published his sole work, the highly influential Reflections on the Motive Power of Fire (1824), in which he discussed heat engines scientifically.

In Reflections, Carnot offered the first definition of work in terms of physics, describing it as "weight lifted through a height." Analyzing Watt's steam engine, he also conducted groundbreaking studies in the nascent science of thermodynamics. Every heat engine, he explained, has a theoretical limit of efficiency related to the temperature difference in the engine: the greater the difference between the lowest and highest temperature, the more efficient the engine.

Carnot's work influenced the development of more efficient steam engines, and also had an impact on the studies of other physicists investigating the relationship between work, heat, and energy. Among these was William Thomson, Lord Kelvin (1824-1907). In addition to coining the term "thermodynamics," Kelvin developed the Kelvin scale of absolute temperature and established the value of absolute zero, equal to −273.15°C or −459.67°F.

According to Carnot's theory, maximum effectiveness was achieved by a machine that could reach absolute zero. However, later developments in the understanding of thermodynamics, as discussed below, proved that both maximum efficiency and absolute zero are impossible to attain.


It is easy to understand that a steam engine is a heat engine: after all, it produces heat. But how is it that a refrigerator, an air conditioner, and other cooling machines are also heat engines? Moreover, given the fact that cold is the absence of heat and heat is energy, one might ask how a refrigerator or air conditioner can possibly use energy to produce cold, which is the same as the absence of energy. In fact, cooling machines simply reverse the usual process by which heat engines operate, and for this reason, they are called "reverse heat engines." Furthermore, they use energy to extract heat.

A steam engine takes heat from a high-temperature reservoir—the place where the water is turned into steam—and uses that energy to produce work. In the process, energy is lost and the heat moves to a low-temperature reservoir, where it condenses to form relatively cool water. A refrigerator, on the other hand, pulls heat from a low-temperature reservoir called the evaporator, into which flows heat from the refrigerated compartment—the place where food and other perishables are kept. The coolant from the evaporator take this heat to the condenser, a high-temperature reservoir at the back of the refrigerator, and in the process it becomes a gas. Heat is released into the surrounding air; this is why the back of a refrigerator is hot.

Instead of producing a work output, as a steam engine does, a refrigerator requires a work input—the energy supplied via the wall outlet. The principles of thermodynamics show that heat always flows from a high-temperature to a low-temperature reservoir, and reverse heat engines do not defy these laws. Rather, they require an external power source in order to effect the transfer of heat from a low-temperature reservoir, through the gases in the evaporator, to a high-temperature reservoir.

The Laws of Thermodynamics


There are three laws of thermodynamics, which provide parameters as to the operation of thermal systems in general, and heat engines in particular. The history behind the derivation of these laws is discussed in the essay on Thermodynamics; here, the laws themselves will be examined in brief form.

The physical law known as conservation of energy shows that within a system isolated from all outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. The first law of thermodynamics states the same fact in a somewhat different manner.

According to the first law of thermodynamics, because the amount of energy in a system remains constant, it is impossible to perform work that results in an energy output greater than the energy input. Thus, it could be said that the conservation of energy law shows that "the glass is half full": energy is never lost. On the hand, the first law of thermodynamics shows that "the glass is half empty": no machine can ever produce more energy than was put into it. Hence, a perpetual motion machine is impossible, because in order to keep a machine running continually, there must be a continual input of energy.


The second law of thermodynamics begins from the fact that the natural flow of heat is always from a high-temperature to a low-temperature reservoir. As a result, no engine can be constructed that simply takes heat from a source and performs an equivalent amount of work: some of the heat will always be lost. In other words, it is impossible to build a perfectly efficient engine.

In effect, the second law of thermodynamics compounds the "bad news" delivered by the first law with some even worse news: though it is true that energy is never lost, the energy available for work output will never be as great as the energy put into a system. Linked to the second law is the concept of entropy, the tendency of natural systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated. "Dissipated" in this context means that the high-and low-temperature reservoirs approach equal temperatures, and as this occurs, entropy increases.


Entropy also plays a part in the third law of thermodynamics, which states that at the temperature of absolute zero, entropy also approaches zero. This might seem to counteract the "worse news" of the second law, but in fact, what the third law shows is that absolute zero is impossible to reach.

As stated earlier, Carnot's engine would achieve perfect efficiency if its lowest temperature were the same as absolute zero; but the second law of thermodynamics shows that a perfectly efficient machine is impossible. Relativity theory (which first appeared in 1905, the same year as the third law of thermodynamics) showed that matter can never exceed the speed of light. In the same way, the collective effect of the second and third laws is to prove that absolute zero—the temperature at which molecular motion in all forms of matter theoretically ceases—can never be reached.


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