Thermodynamics and the Theory of Heat

The nature of heat has been a major subject for study since the beginnings of modern science. Early investigators, including Galileo, Boyle, and Newton, explained heat as the motion of tiny particles of which bodies are made. In the 18th century scientists advanced understanding by concentrating on the flow of heat. It was thought of as a fluid, and experiments were made on the heat conductivity of metals.


Antoine Lavoisier attempted to develop a quantitative theory of heat. He showed that the heat produced in chemical reactions could be studied quantitatively. He developed a system of thermodynamics that helped to explain the relations between heat and chemical reactions. Lavoisier's theories were still based on the idea that heat was a fluid.


THERMODYNAMICS

The study of heat energy made great strides during the industrial age when steam engines were a primary means of harnessing energy to do work. Thermodynamics, from the Latin for "motion of heat," is the term used by physicists for the study of the movement of heat energy.


The Laws of Thermodynamics are accepted generalizations that describe the fundamentals of heat energy movement. Stated simply, the first two are as follows:

 

  • The First Law of Thermodynamics states that in a closed system total energy is constant or conserved. It is often called the law of conservation of energy. What it means, in a simple example, is that the energy in a gallon of gasoline must equal the work produced by the car burning the gallon of gasoline, including the motion, chemical, friction, heat, electrical, and noise energies/work. Nothing is lost and nothing is left unaccounted for.
  • The Second Law of Thermodynamics asserts that in a closed system heat energy flows only from warmer to cooler regions, unless work is done to move it in the other direction. Isaac Asirnov, in his book Understanding Physics, says that another way to state these laws is that "the first law says 'You can't win,' and the second law adds, 'And you can't break even, either.'"

A branch of physics that assumed major stature during the 19th century was thermodynamics. It began by disentangling the previously confused concepts of heat and temperature, by arriving at meaningful definitions, and by showing how they could be related to the heretofore purely mechanical concepts of work and energy.


Thermodynamics is the field of physics that describes and correlates the physical properties of macroscopic systems of matter and energy. The principles of thermodynamics are of fundamental importance to all branches of science and engineering.


A central concept of thermodynamics is that of the macroscopic system, defined as a geometrically insoluble piece of matter in coexistence with an infinite, unperturbable environment. The state of a macroscopic system in equilibrium can be described in terms of such measurable properties as temperature, pressure, and volume, which are known as thermodynamic variables. Many other variables (such as density, specific heat, compressibility, and the coefficient of thermal expansion) can be identified and correlated to produce a more complete description of an object and its relationship to its environment.


When a macroscopic system moves from one state of equilibrium to another, a thermodynamic process is said to take place. Some processes are reversible and others are irreversible. The laws of thermodynamics, discovered in the 19th century through painstaking experimentation, govern the nature of all thermodynamic processes and place limits on them.


Zeroth Law of Thermodynamics

The vocabulary of empirical sciences is often borrowed from daily language. Thus, although the term temperature appeals to common sense, its meaning suffers from the imprecision of nonmathematical language. A precise, though empirical, definition of temperature is provided by the so-called zeroth law of thermodynamics as explained below.


When two systems are in equilibrium, they share a certain property. This property can be measured and a definite numerical value ascribed to it. A consequence of this fact is the zeroth law of thermodynamics, which states that when each of two systems is in equilibrium with a third, the first two systems must be in equilibrium with each other. This shared property of equilibrium is the temperature.


If any such system is placed in contact with an infinite environment that exists at some certain temperature, the system will eventually come into equilibrium with the environment—that is, reach the same temperature. (The so-called infinite environment is a mathematical abstraction called a thermal reservoir. In reality, the environment need only be large relative to the system being studied.)


First Law of Thermodynamics

The first law of thermodynamics gives a precise definition of heat, another commonly used concept.

When an object is brought into contact with a relatively colder object, a process takes place that brings about an Caroot equalization of temperatures of the two objects.


To explain this phenomenon, 18th-century scientists hypothesized that a substance more abundant at higher temperature flowed toward the region at a lower temperature. This hypothetical substance, called "caloric," was thought to be a fluid capable of moving through material media.


The first law of thermodynamics instead identifies caloric, or heat, as a form of energy. It can be converted into mechanical work, and it can be stored, but is not a material substance. Heat, measured originally in terms of a unit called the calorie, and work and energy, measured in ergs, were shown by experiment to be totally equivalent. One calorie is equivalent to 4.186 x 107 ergs, or 4.186 joules.


The first law, then, is a law of energy conservation. It states that, because destroyed—setting aside the later ramifications of the equivalence of mass and energy—the amount of heat transferred into a system plus the amount of work done on the system must result in a corresponding increase of internal energy in the system. Heat and work are mechanisms by which systems exchange energy with one another.


In any machine, some amount of energy is converted into work; therefore, no machine can exist in which no energy is converted into work. Such a hypothetical machine (in which no energy is required for performing work) is termed a perpetual-motion machine of the first kind. Since the input energy must now take heat into account (and in a broader sense chemical, electrical, nuclear, and other forms of energy as well), the law of
energy conservation rules out the possibility of such a machine ever being invented. The first law is sometimes given in a contorted form as a statement that precludes the existence of perpetual- motion machines of the first kind.


The equivalence of heat and work was explained by the German physicist Hermann Ludwig Ferdinand von Helmholtz and the British mathematician and physicist William Thomson, 1st Baron Kelvin, by the middle of the 19th century. Equivalence means that doing work on a system can produce exactly the same effect as adding heat; thus the same temperature rise can be achieved in a gas contained in a vessel by adding heat or by doing an appropriate amount of work through a paddle wheel sticking into the container where the paddle
is actuated by falling weights.

The numerical value of this equivalent was first demonstrated by the British physicist James Prescott Joule in several heating and paddle-wheel experiments between 1840 and 1849. It was recognized that performing work or adding heat to a system were both means of transferring energy to it was thus recognized. Therefore, the amount of energy added by heat or work had to increase the internal energy of the system, which in turn
determined the temperature. If the internal energy remains unchanged, the amount of work done on a system must equal the heat given up by it. This is the first law of thermodynamics, a statement of the conservation of energy. Not until the action of molecules in a system was better understood by the development of the kinetic theory could this internal energy be related to the sum of the kinetic energies of all the molecules
making up the system.


Second Law of Thermodynamics

The second law of thermodynamics gives a precise definition of a property called entropy. Entropy can be thought of as a measure of how close a system is to equilibrium. It can also be thought of as a measure of the disorder in the system. The law states that the entropy—that is, the disorder—of an isolated system can never decrease. Thus, when an isolated system achieves a configuration of maximum entropy, it can no longer undergo change. It has reached equilibrium. Nature, then, seems to "prefer" disorder or chaos. It can be shown that the second law stipulates that, in the absence of work, heat cannot be transferred from a region at a lower temperature to one at a higher temperature.


The second law poses an additional condition on thermodynamic processes. It is not enough to conserve energy and thus obey the first law. A machine that would deliver work while violating the second law is called a "perpetual-motion machine of the second kind," since, for example, energy could then be continually drawn from a cold environment to do work in a hot environment at no cost. The second law of thermodynamics is sometimes given as a statement that precludes perpetual- motion machines of the second kind.


While the first law indicates that energy must be conserved in any interactions between a system and its surroundings, it gives no indication whether all forms of mechanical and thermal energy exchange are possible. That overall changes in energy proceed in one direction was first formulated by the French physicist and military engineer Nicolas Leonard Sadi Camot, who in 1824 pointed out that a heat engine (a device that
can produce work continuously while only exchanging heat with its surroundings) requires both a hot body as a source of heat and a cold body to absorb heat that must be discharged. When the engine performs work, heat must be transferred from the hotter to the colder body; to have the inverse take place requires the expenditure of mechanical (or electrical) work. Thus, in a continuously working refrigerator, the absorption
of heat from the low temperature source (the cold space) requires the addition of work (usually as electrical power) and the discharge of heat (usually via finned coils in the rear) to the surroundings. These ideas, based on Camot's concepts, were eventually formulated rigorously as the second law of thermodynamics by the German mathematical physicist Rudolf Julius Emanuel Clausius and by Lord Kelvin in various alternate,
although equivalent, ways. One such formulation is that heat cannot flow from a colder to a hotter body without the expenditure of work.


From the second law, it follows that in an isolated system (one that has no interactions with the surroundings) internal portions at different temperatures will always adjust to a single uniform temperature and thus produce equilibrium. This can also be applied to other internal properties that may be different initially. If milk is poured into a cup of coffee, for example, the two substances will continue to mix until they are
inseparable and can no longer be differentiated. Thus, an initial separate or ordered state is turned into a mixed or disordered state. These ideas can be expressed by a thermodynamic property, called the entropy (first formulated by Clausius), which serves as a measure of how close a system is to equilibrium, that is, to perfect internal disorder. The entropy of an isolated system, and of the universe as a whole, can only
increase, and when equilibrium is eventually reached, no more internal change of any form is possible. Applied to the universe as a whole, this principle suggests that eventually all temperature in space becomes uniform, resulting in the so-called heat death of the universe.


Locally, the entropy can be lowered by external action. This applies to machines, such as a refrigerator, where the entropy in the cold chamber is being reduced, and to living organisms. This local increase in order is, however, only possible at the expense of an entropy increase in the surroundings; here more disorder must be created.


This continued increase in entropy is related to the observed nonreversibility of macroscopic processes. If a process were spontaneously reversible, that is, if after having undergone a process both it and all the surroundings could be brought back to their initial state, the entropy would remain constant in violation of the second law. While this is true for macroscopic processes, and therefore corresponds to daily experience,
it does not apply to microscopic processes, which are believed to be reversible. Thus, chemical reactions between individual molecules are not governed by the second law, which applies only to macroscopic ensembles.


From the promulgation of the second law, thermodynamics went on to other advances and applications in physics, chemistry, and engineering. Most chemical engineering, all power-plant engineering, and air conditioning and low-temperature physics are just a few of the fields that owe their theoretical basis to thermodynamics and to the subsequent achievements of such scientists as Maxwell, the American physicist
Willard Gibbs, the German physical chemist Walther Hermann Nernst, and the Norwegian-born American chemist Lars Onsager (1903-76).


Thermodynamic Cycles

All important thermodynamic relations used in engineering are derived from the first and second laws of thermodynamics. One useful way of discussing thermodynamic processes is in terms of cycles—processes that return a system to its original state after a number of stages, thus restoring the original values for all the relevant thermodynamic variables. In a complete cycle the internal energy of a system depends solely on
these variables and cannot change. Thus, the total net heat transferred to the system must equal the total net work delivered from the system.


An ideal cycle would be performed by a perfectly efficient heat engine. All the heat would be converted to mechanical work. The 19th-century French scientist Nicolas Leonard Sadi Carnot, who conceived a thermodynamic cycle that is the basic cycle of all heat engines, showed that such an ideal engine cannot exist. Any heat engine must expend some fraction of its heat input as exhaust. The second law of thermodynamics places an upper limit on the efficiency of engines; that upper limit is less than 100 percent. The limiting case is now known as a Camot cycle.


Third Law of Thermodynamics

The second law suggests the existence of an absolute temperature scale that includes an absolute zero of temperature. The third law of thermodynamics states that absolute zero cannot be attained by any procedure in a finite number of steps. Absolute zero can be approached arbitrarily closely, but it can never be reached.


Microscopic Basis of Thermodynamics

The recognition that all matter is made up of molecules provided a microscopic foundation for thermodynamics. A thermodynamic system consisting of a pure substance can be described as a collection of like molecules, each with its individual motion describable in terms of such mechanical variables as velocity and momentum. At least in principle, it should therefore be possible to derive the collective properties of the
system by solving equations of motion for the molecules. In this sense, thermodynamics could be regarded as a mere application of the laws of mechanics to the microscopic system.

 

Objects of ordinary size—that is, ordinary on the human scale—contain immense numbers (on the order of 1024) of molecules. Assuming the molecules to be spherical, each would need three variables to describe its position and three more to describe its velocity. Describing a macroscopic system in this way would be a task that even the largest modern computer could not manage. A complete solution of these equations, furthermore, would tell us where each molecule is and what it is doing at every moment. Such a vast quantity of information would be too detailed to be useful and too transient to be important.


Statistical methods were devised therefore to obtain averages of the mechanical variables of the molecules in a system and to provide the gross features of the system. These gross features turn out to be, precisely, the macroscopic thermodynamic variables. The statistical treatment of molecular mechanics is called statistical mechanics, and it anchors thermodynamics to mechanics.


Viewed from the statistical perspective, temperature represents a measure of the average kinetic energy of the molecules of a system. Increases in temperature reflect increases in the vigor of molecular motion. When two systems are in contact, energy is transferred between molecules as a result of collisions. The transfer will continue until uniformity is achieved, in a statistical sense, which corresponds to thermal equilibrium. The
kinetic energy of the molecules also corresponds to heat and—together with the potential energy arising from interaction between molecules—makes up the internal energy of a system.


The conservation of energy, a well- known law of mechanics, translates readily to the first law of thermodynamics, and the concept often translates into the extent of disorder on the molecular scale. By assuming that all combinations of molecular motion are equally likely, thermodynamics shows that the more disordered the state of an isolated system, the more combinations can be found that could give rise to that
state, and hence the more frequently it will occur. The probability of the more disordered state occurring overwhelms the probability of the occurrence of all other states. This probability provides a statistical basis for definitions of both equilibrium state and entropy.


Finally, temperature can be reduced by taking energy out of a system, that is, by reducing the vigor of molecular motion. Absolute zero corresponds to the state of a system in which all its constituents are at rest. This is, however, a notion from classical physics. In terms of quantum mechanics, residual molecular motion will exist even at absolute zero. An analysis of the statistical basis of the third law goes beyond the scope of the present discussion.


Expansion and Contraction with Heat

All matter increases in volume when there is an increase in temperature. In the case of gases the increase is a large one. If the pressure and the weight of gas remain the same, the increase in volume will be in direct proportion to the increase in temperature. The application of heat to a solid causes it to expand also but to a much smaller degree than a gas. In a metal rod every unit length of the rod becomes longer when it expands. The increase in length for each unit of length per degree rise in temperature is called the coefficient of linear expansion. Liquids in general behave like solids and expand slightly when the temperature is raised.


The Transfer of Heat

Heat transfer helps to shape the world in which we live. Great loss is suffered by man when heat transfer is impossible. If a way could be found to transfer heat to the polar regions they could support large populations just as the temperate countries do. Fortunately man has been more successful in making use of the natural methods of heat transfer on a smaller scale. A quantity of heat is useless if it is where it is not needed. It may be useful if it can be moved to another place.


Heat, by its very nature, helps to make this possible. Heat always travels, or flows, from a high temperature to a low temperature. It can do this by three different methods. These are called conduction, convection, and radiation.


Heat Transfer

Heat Transfer, in physics, is the process by which energy in the form of heat is exchanged between bodies or parts of the same body at different temperatures. Heat is generally transferred by convection, radiation, or conduction. Although these three processes can occur simultaneously, it is not unusual for one mechanism to overshadow the other two. Heat, for example, is transferred by conduction through the brick wall of a house,
the surfaces of high-speed aircraft are heated by convection, and the earth receives heat from the sun by radiation.


Three Modes of Heat Transfer

  • Conduction
  • Convection
  • Radiation