Thermodynamics - How it works
H ISTORICAL C ONTEXT
Machines were, by definition, the focal point of the Industrial Revolution, which began in England during the late eighteenth and early nineteenth centuries. One of the central preoccupations of both scientists and industrialists thus became the efficiency of those machines: the ratio of output to input. The more output that could be produced with a given input, the greater the production, and the greater the economic advantage to the industrialists and (presumably) society as a whole.
At that time, scientists and captains of industry still believed in the possibility of a perpetual motion machine: a device that, upon receiving an initial input of energy, would continue to operate indefinitely without further input. As it emerged that work could be converted into heat, a form of energy, it began to seem possible that heat could be converted directly back into work, thus making possible the operation of a perfectly reversible perpetual motion machine. Unfortunately, the laws of thermodynamics dashed all those dreams.
SNOW'S EXPLANATION.
Some texts identify two laws of thermodynamics, while others add a third. For these laws, which will be discussed in detail below, British writer and scientist C. P. Snow (1905-1980) offered a witty, nontechnical explanation. In a 1959 lecture published as The Two Cultures and the Scientific Revolution, Snow compared the effort to transform heat into energy, and energy back into heat again, as a sort of game.
The first law of thermodynamics, in Snow's version, teaches that the game is impossible to win. Because energy is conserved, and thus, its quantities throughout the universe are always the same, one cannot get "something for nothing" by extracting more energy than one put into a machine.
The second law, as Snow explained it, offers an even more gloomy prognosis: not only is it impossible to win in the game of energy-work exchanges, one cannot so much as break even. Though energy is conserved, that does not mean the energy is conserved within the machine where it is used: mechanical systems tend toward increasing disorder, and therefore, it is impossible
The third law, discovered in 1905, seems to offer a possibility of escape from the conditions imposed in the second law: at the temperature of absolute zero, this tendency toward breakdown drops to a level of zero as well. But the third law only proves that absolute zero cannot be attained: hence, Snow's third observation, that it is impossible to step outside the boundaries of this unwinnable heat-energy transformation game.
W ORK AND E NERGY
Work and energy, discussed at length elsewhere in this volume, are closely related. Work is the exertion of force over a given distance to displace or move an object. It is thus the product of force and distance exerted in the same direction. Energy is the ability to accomplish work.
There are many manifestations of energy, including one of principal concern in the present context: thermal or heat energy. Other manifestations include electromagnetic (sometimes divided into electrical and magnetic), sound, chemical, and nuclear energy. All these, however, can be described in terms of mechanical energy, which is the sum of potential energy—the energy that an object has due to its position—and kinetic energy, or the energy an object possesses by virtue of its motion.
MECHANICAL ENERGY.
Kinetic energy relates to heat more clearly than does potential energy, discussed below; however, it is hard to discuss the one without the other. To use a simple example—one involving mechanical energy in a gravitational field—when a stone is held over the edge of a cliff, it has potential energy. Its potential energy is equal to its weight (mass times the acceleration due to gravity) multiplied by its height above the bottom of the canyon below. Once it is dropped, it acquires kinetic energy, which is the same as one-half its mass multiplied by the square of its velocity.
Just before it hits bottom, the stone's kinetic energy will be at a maximum, and its potential energy will be at a minimum. At no point can the value of its kinetic energy exceed the value of the potential energy it possessed before it fell: the mechanical energy, or the sum of kinetic and potential energy, will always be the same, though the relative values of kinetic and potential energy may change.
CONSERVATION OF ENERGY.
What mechanical energy does the stone possess after it comes to rest at the bottom of the canyon? In terms of the system of the stone dropping from the cliffside to the bottom, none. Or, to put it another way, the stone has just as much mechanical energy as it did at the very beginning. Before it was picked up and held over the side of the cliff, thus giving it potential energy, it was presumably sitting on the ground away from the edge of the cliff. Therefore, it lacked potential energy, inasmuch as it could not be "dropped" from the ground.
If the stone's mechanical energy—at least in relation to the system of height between the cliff and the bottom—has dropped to zero, where did it go? A number of places. When it hit, the stone transferred energy to the ground, manifested as heat. It also made a sound when it landed, and this also used up some of its energy. The stone itself lost energy, but the total energy in the universe was unaffected: the energy simply left the stone and went to other places. This is an example of the conservation of energy, which is closely tied to the first law of thermodynamics.
But does the stone possess any energy at the bottom of the canyon? Absolutely. For one thing, its mass gives it an energy, known as mass or rest energy, that dwarfs the mechanical energy in the system of the stone dropping off the cliff. (Mass energy is the other major form of energy, aside from kinetic and potential, but at speeds well below that of light, it is released in quantities that are virtually negligible.) The stone may have electromagnetic potential energy as well; and of course, if someone picks it up again, it will have gravitational potential energy. Most important to the present discussion, however, is its internal kinetic energy, the result of vibration among the molecules inside the stone.
H EAT AND T EMPERATURE
Thermal energy, or the energy of heat, is really a form of kinetic energy between particles at the atomic or molecular level: the greater the movement of these particles, the greater the thermal energy. Heat itself is internal thermal energy that flows from one body of matter to another. It is not the same as the energy contained in a system—that is, the internal thermal energy of the system. Rather than being "energy-in-residence," heat is "energy-in-transit."
This may be a little hard to comprehend, but it can be explained in terms of the stone-and-cliff kinetic energy illustration used above. Just as a system can have no kinetic energy unless something is moving within it, heat exists only when energy is being transferred. In the above illustration of mechanical energy, when the stone was sitting on the ground at the top of the cliff, it was analogous to a particle of internal energy in body A. When, at the end, it was again on the ground—only this time at the bottom of the canyon—it was the same as a particle of internal energy that has transferred to body B. In between, however, as it was falling from one to the other, it was equivalent to a unit of heat.
TEMPERATURE.
In everyday life, people think they know what temperature is: a measure of heat and cold. This is wrong for two reasons: first, as discussed below, there is no such thing as "cold"—only an absence of heat. So, then, is temperature a measure of heat? Wrong again.
Imagine two objects, one of mass M and the other with a mass twice as great, or 2 M. Both have a certain temperature, and the question is, how much heat will be required to raise their temperature by equal amounts? The answer is that the object of mass 2 M requires twice as much heat to raise its temperature the same amount. Therefore, temperature cannot possibly be a measure of heat.
What temperature does indicate is the direction of internal energy flow between bodies, and the average molecular kinetic energy in transit between those bodies. More simply, though a bit less precisely, it can be defined as a measure of heat differences. (As for the means by which a thermometer indicates temperature, that is beyond the parameters of the subject at hand; it is discussed elsewhere in this volume, in the context of thermal expansion.)
MEASURING TEMPERATURE AND HEAT.
Temperature, of course, can be measured either by the Fahrenheit or Centigrade scales familiar in everyday life. Another temperature scale of relevance to the present discussion is the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907).
Drawing on the discovery made by French physicist and chemist J. A. C. Charles (1746-1823), that gas at 0°C (32°F) regularly contracts by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (discussed below) as −273.15°C (−459.67°F). The Kelvin and Celsius scales are thus directly related: Celsius temperatures can be converted to Kelvins (for which neither the word nor the symbol for "degree" are used) by adding 273.15.
MEASURING HEAT AND HEAT CAPACITY.
Heat, on the other hand, is measured not by degrees (discussed along with the thermometer in the context of thermal expansion), but by the same units as work. Since energy is the ability to perform work, heat or work units are also units of energy. The principal unit of energy in the SI or metric system is the joule (J), equal to 1 newton-meter (N · m), and the primary unit in the British or English system is the foot-pound (ft · lb). One foot-pound is equal to 1.356 J, and 1 joule is equal to 0.7376 ft · lb.
Two other units are frequently used for heat as well. In the British system, there is the Btu, or British thermal unit, equal to 778 ft · lb. or 1,054 J. Btus are often used in reference, for instance, to the capacity of an air conditioner. An SI unit that is also used in the United States—where British measures typically still prevail—is the kilocalorie. This is equal to the heat that must be added to or removed from 1 kilogram of water to change its temperature by 1°C. As its name suggests, a kilocalorie is 1,000 calories. A calorie is the heat required to change the temperature in 1 gram of water by 1°C—but the dietary Calorie (capital C), with which most people are familiar is the same as the kilocalorie.
A kilocalorie is identical to the heat capacity for one kilogram of water. Heat capacity (sometimes called specific heat capacity or 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. this is measured in units of J/kg · °C (joules per kilogram-degree Centigrade), though for the sake of convenience it is typically rendered in terms of kilojoules (1,000 joules): kJ/kg · °c. Expressed thus, the specific heat of water 4.185—which is fitting, since a kilocalorie is equal to 4.185 kJ. Water is unique in many aspects, with regard to specific heat, in that it requires far more heat to raise the temperature of water than that of mercury or iron.