thermodynamics branch of science concerned with the nature of heat and its conversion to mechanical, electric, and chemical energy . Historically, it grew out of efforts to construct more efficient heat engines—devices for extracting useful work from expanding hot gases.

The Thermodynamic System and Its Environment

In thermodynamics, one usually considers both the thermodynamic system and its environment. The environment often contains one or more idealized heat reservoirs—heat sources with infinite heat capacity enabling them to give up or absorb heat without changing their temperature. (An ocean or other large body of water approximates a heat reservoir.) A typical thermodynamic system is a definite quantity of gas enclosed in a cylinder with a sliding piston that allows the volume to vary. In general, a thermodynamic system is defined by its temperature, volume, pressure, and chemical composition. A system is in equilibrium when these variables have the same value at all points.

A mathematical statement that links the variables to show their interdependence is called an equation of state; the gas laws are simple examples of such equations. Equations of state take on their simplest form when the Kelvin temperature scale is used; on this scale 0° corresponds to the lowest temperature theoretically possible.

When the external conditions are altered, a thermodynamic system will respond by changing its state; the temperature, volume, pressure, and chemical composition will adjust to a new equilibrium. The most important kinds of changes are adiabatic and isothermal changes. An adiabatic change is one that occurs without any flow of heat. The system is thermally insulated from the environment, and the first law of thermodynamics requires that the work done by or on the system be equal to the loss or gain of the system's internal energy. An isothermal change occurs when the system is in contact with a heat reservoir, so that the system remains at the temperature of the reservoir. In the isothermal process, heat flows from the reservoir if the system is expanding and into the reservoir if the system is being compressed. For an ideal gas the internal energy depends only on the temperature; hence the internal energy remains constant during an isothermal change, and the heat absorbed from or by the reservoir is equal to the work done on or by the environment.

The First Law of Thermodynamics

Toward the middle of the 19th cent. heat was recognized as a form of energy associated with the motion of the molecules of a body (see kinetic-molecular theory of gases ). Speaking more strictly, heat refers only to energy that is being transferred from one body to another. The total energy a body contains as a result of the positions and motions of its molecules is called its internal energy; in general, a body's temperature is a direct measure of its internal energy. All bodies can increase their internal energies by absorbing heat (see heat capacity ). However, mechanical work done on a body can also increase its internal energy; e.g., the internal energy of a gas increases when the gas is compressed. Conversely, internal energy can be converted into mechanical energy; e.g., when a gas expands it does work on the external environment. In general, the change in a body's internal energy is equal to the heat absorbed from the environment minus the work done on the environment. This statement constitutes the first law of thermodynamics, which is a general form of the law of conservation of energy (see conservation laws ).

The Second Law of Thermodynamics

A cyclic process is one that returns the system, but not the environment, to its original state. A closed cycle consisting of two isothermal and two adiabatic transformations is called a Carnot cycle after the French physicist Sadi Carnot , who first discussed the implications of such cycles. During the Carnot cycle occurring in the operation of a heat engine, a definite quantity of heat is absorbed from a reservoir at high temperature; part of this heat is converted into useful work, but the balance is expelled into a low-temperature reservoir and thus "wasted." The greater the temperature difference between the two reservoirs, which in a steam engine are represented by the boiler and the condenser, the greater the fraction of absorbed heat that is converted into useful work. It is, however, theoretically impossible to convert all the heat extracted from the reservoir into useful work.

In general it is impossible to perform a transformation whose only final result is to convert into useful work heat extracted from a source that is at the same temperature throughout. This statement is Lord Kelvin's version of the second law of thermodynamics. Another version of this law, formulated by R. J. E. Clausius, states that a transformation is impossible whose only final result is to transfer heat from a body at a given temperature to a body at higher temperature; in other words, the spontaneous flow of heat from hot to cold bodies is reversible only with the expenditure of mechanical or other nonthermal energy. These two versions of the second law of thermodynamics can be shown to be entirely equivalent.

The second law is expressed mathematically in terms of the concept of entropy . When a body absorbs an amount of heat Q from a reservoir at temperature T, the body gains and the reservoir loses an amount of entropy S = Q/T. Thus, in a reversible adiabatic process (no heat change) there is no change in the total entropy. If an amount of heat Q flows from a hot to a cold body, the total entropy increases; because S = Q/T is larger for smaller values of T, the cold body gains more entropy than the hot body loses. The statement that heat never flows from a cold to a hot body can be generalized by saying that in no spontaneous process does the total entropy decrease.

In all real physical processes entropy increases; in ideal reversible processes entropy remains constant. Thus, in the Carnot cycle, which is reversible, there is no change in the total entropy. The engine itself experiences no net change in entropy because it is returned to its original state at the end of the cycle. The entropy gained by the low temperature reservoir is equal to the entropy lost by the high temperature reservoir. However, according to the formula S = Q/T, less heat need be expelled into the low temperature reservoir than is extracted from the high temperature reservoir for equal and opposite changes in entropy. In the Carnot cycle this difference in heat appears as useful mechanical work.

The Third Law of Thermodynamics

A postulate related to but independent of the second law is that it is impossible to cool a body to absolute zero by any finite process. Although one can approach absolute zero as closely as one desires, one cannot actually reach this limit. The third law of thermodynamics, formulated by Walter Nernst and also known as the Nernst heat theorem, states that if one could reach absolute zero, all bodies would have the same entropy. In other words, a body at absolute zero could exist in only one possible state, which would possess a definite energy, called the zero-point energy. This state is defined as having zero entropy.

Bibliography

See E. Fermi, Thermodynamics (1937); F. W. Sears, Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics (2d ed. 1953); M. W. Zemansky, Heat and Thermodynamics (5th ed. 1968).

Thermodynamics

Thermodynamics is the science of heat and temperature and, in particular, of the laws governing the conversion of thermal energy into mechanical, electrical, or other forms of energy. It is a central branch of science that has important applications in chemistry, physics, biology, and engineering. Thermodynamics is a logical discipline that organizes the information obtained from experiments performed on systems and enables us to draw conclusions, without further experimentation, about other properties of the system. It allows us to predict whether a reaction will proceed and what the maximum yield might be.

Thermodynamics is a macroscopic science that deals with such properties as pressure, temperature, and volume. Unlike quantum mechanics , thermodynamics is not based on a specific model, and therefore it is unaffected by our changing concepts of atoms and molecules. By the same token, equations derived from thermodynamics do not provide us with molecular interpretations of complex phenomena. Furthermore, thermodynamics tells us nothing about the rate of a process except its likelihood.

Applications of thermodynamics are based on three fundamental laws that deal with energy and entropy changes. The laws of thermodynamics cannot be derived; their validity is based on the fact that they predict changes that are consistent with experimental observations.

The first law of thermodynamics is based on the law of conservation of energy, which states that energy can neither be created nor destroyed; therefore, the total energy of the universe is constant. It is convenient for scientists to divide the universe into two parts: the system (the part of the universe that is under study—for example, a beaker of solution) and the surroundings (the rest of the universe). For any process, then, the change in the energy of the universe is zero. Chemists are usually interested only in what happens to the system. Consequently, for a given process the first law can be expressed as

ΔU = q + w          (1)

where ΔU is the change in the internal energy of the system, q is the heat exchange between the system and the surroundings, and w is the work done by the system or performed on the system by the surroundings. The first law is useful in studying the energetics of physical processes, such as the melting or boiling of a substance, and chemical reactions—for example, combustion . The heat change occurring as part of a process is measured with a calorimeter. For a constant-volume process, the heat change is equated to the change in the internal energy ΔU of the system; for a constant-pressure process, which is more common, the heat change is equated to the change in the enthalpy ΔH of the system. Enthalpy H is a thermodynamic function closely related to the internal energy of the system, and is defined as

H = U + PV          (2)

where P and V are the pressure and volume of the system, respectively.

The first law of thermodynamics deals only with energy changes and cannot predict the direction of a process. It asks, for example: Under a given set of conditions of pressure, temperature, and concentration, will a specific reaction occur? To answer the question we need a new thermodynamic function called entropy S. To define entropy, we need to use a quantum mechanical concept. The entropy of a system is related to the distribution of energy among the available molecular energy levels at a given temperature. The greater the number of energy levels that have significant occupation, the greater the entropy.

The second law of thermodynamics states that the entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. The mathematical statement of the second law of thermodynamics is given by

ΔS _univ = ΔS _sys + ΔS _surr ≥ 0          (3)

where the subscripts denote the universe, the system, and the surroundings, respectively. The greater than portion of the "greater than or equal to" sign corresponds to a spontaneous process, and the equal portion corresponds to a system at equilibrium. Because processes in the real world are spontaneous, the entropy of the universe therefore constantly increases with time.

As is not the case with energy and enthalpy , it is possible to determine the absolute value of entropy of a system. To measure the entropy of a substance at room temperature, it is necessary to add up entropy from the absolute zero up to 25°C (77°F). However, the absolute zero is unattainable in practice. This dilemma is resolved by applying the third law of thermodynamics, which states that the entropy of a pure, perfect crystalline substance is zero at the absolute zero of temperature. The increase in entropy from the lowest reachable temperature upward can then be determined from heat capacity measurements and enthalpy changes due to phase transitions.

Because it is inconvenient to use the change in entropy of the universe to determine the direction of a reaction, an additional thermodynamic function, called the Gibbs free energy (G ), is introduced to help chemists to focus only on the system. The Gibbs free energy of a system is defined as G = H − TS, where T is the absolute temperature. At constant temperature and pressure, ΔG is negative for a spontaneous process, is positive for an unfavorable process, and equals zero for a system at equilibrium. The change in Gibbs free energy can be related to the changes in enthalpy and entropy of a reaction, and also to the equilibrium constant of the reaction, according to the equation ΔG ° = −RT ln K, where ΔG ° is the change in Gibbs free energy under standard-state conditions (1 bar), R is the gas constant, and K is the equilibrium constant.

Many chemical reactions can be classified as either kinetically controlled or thermodynamically controlled. In a kinetically controlled process the products are thermodynamically more stable than the reactants, hence the reaction is favorable. However, the rate of reaction is often very slow due to a high activation energy barrier. The conversion of the less stable allotropic form of carbon, diamond, to the more stable graphite is an example: The process can take millions of years to complete. In a thermodynamically controlled reaction the reactants may have a number of kinetically accessible routes to follow to form different products, but what is eventually formed is governed by relative thermodynamic stability. In protein folding, for example, a denatured protein may have many possibilities of intermediate conformation; however, the conformation it finally assumes, which corresponds to the physiologically functioning protein, is the most stable state thermodynamically.

see also Chemistry and Energy; Energy; Heat; Kinetics; Physical Chemistry; Temperature.

Raymond Chang

Bibliography

Bent, Henry A. (1965). The Second Law: An Introduction to Classical and Statistical Thermodynamics. New York: Oxford University Press.

Berry, R. Stephen (1991). Understanding Energy: Energy, Entropy, and Thermodynamics for Everyman. River Edge, NJ: World Scientific.

Smith, E. Brian (1990). Basic Chemical Thermodynamics, 4th edition. New York: Oxford University Press.

Thermodynamics

Thermodynamics is the science that deals with work and heat—and the transformation of one into the other. It is a macroscopic theory, dealing with matter in bulk, disregarding the molecular nature of materials. The corresponding microscopic theory, based on the fact that materials are made up of a vast number of particles, is called statistical mechanics.

Historical background

The origins of thermodynamics can be traced to the late eighteenth century. English-American physicist Benjamin Thomson, Count Rumford (1753–1814), became intrigued by the physical changes accompanying the boring of cannons. (Boring is the process of making a hole—in this case the barrel of the cannon—with a twisting movement.) He found that the work (or mechanical energy) involved in the boring process was converted to heat as a result of friction, causing the temperature of the cannon to rise.

Some of the fundamental relationships involved in thermodynamics were later developed by English physicist James Joule (1818–1889), who showed that work can be converted to heat without limit. Other researchers found, however, that the opposite is not true—that is, that there are limiting factors that operate in the conversion of heat to work. The research of French physicist Sadi Carnot (1796–1832), British physicist William Thomson, Lord Kelvin (1824–1907), and German physicist Rudolf Clausius (1822–1888), among others, has led to an understanding of these limitations.

The laws of thermodynamics

The most basic facts about thermodynamics can be summarized in two general laws. The first law of thermodynamics is actually nothing other than the law of conservation of energy: energy can neither be created nor destroyed. It can be converted from one form to another, but the total amount of energy in a system always remains constant.

For example, consider the simple example of heating a beaker of water with a gas flame. One can measure the amount of heat energy given off by the flame. One also can measure the increase in the heat energy of the water in the beaker, the beaker itself, and any air surrounding the beaker. Under ideal circumstances, the total amount of energy produced by the flame is equal to the total amount of energy gained by the water, the beaker, and the air.

The first law of thermodynamics is sometimes stated in a somewhat different form because of the kinds of systems to which it is applied. Another statement is that the internal energy of a system is equal to the amount of work done on the system plus any heat added to the system. In this definition, the term work is used to describe all forms of energy other than heat.

The first law can be thought of as a quantitative law (involving measurement of some quantity or amount): the amount of energy lost by one system is equal to the amount of energy gained by a second system. The second law, in contrast, can be thought of as a qualitative law (involving quality or kind): the second law says that all natural processes occur in such a way as to result in an increase in entropy.

To understand this law, it is first necessary to explain the concept of entropy. Entropy means disorder. Consider the dissolving of a sugar cube in water. The sugar cube itself represents a highly ordered state in which every sugar particle is arranged in an exact position within the sugar crystal. The entropy of a sugar cube is low because there is little disorder.

Words to Know

Energy: The capacity for doing work.

Entropy: The amount of disorder in a system.

First law of thermodynamics: The internal energy of a system is increased by the amount of work done on the system and the heat flow to the system (Conservation of Energy).

Heat: A form of energy produced by the motion of molecules that make up a substance.

Second law of thermodynamics: All natural processes proceed in a direction that leads to an increase in entropy.

Submicroscopic level of phenomena: Phenomena that cannot be observed directly by any of the five human senses, aided or unaided.

Work: Transfer of energy by a force acting to move matter.

But consider what happens when the sugar cube is dissolved in water. The cube breaks apart, and sugar molecules are dispersed completely throughout the water. There is no longer any order among the sugar molecules at all. The entropy of the system has increased because the sugar molecules have become completely disorganized.

The second law of thermodynamics simply says that any time some change takes place in nature, there will be more entropy—more disorganization—than there was to begin with. As a practical example, consider the process by which electricity is generated in most instances in the United States today. Coal or oil is burned in a large furnace, heating water and changing it to steam. The steam then is used to run turbines and generators that manufacture electricity. The first law of thermodynamics says that all of the energy stored in coal and oil must ultimately be converted to some other form: electricity or heat, for example. But the second law says that some of the energy from coal and oil will end up as "waste" heat, heat that performs no useful function. It is energy that simply escapes into the surrounding environment and is distributed throughout the universe.

The second law is sometimes described as the "death of the universe" law because it means that over very long periods of time, all forms of energy will be evenly distributed throughout the universe. The waste energy produced by countless numbers of natural processes will add up over the millennia until that is the only form in which energy will remain in our universe.

[See also Gases, properties of; Heat; Temperature ]

thermodynamics Branch of physics that studies heat and how it is transformed to and from other forms of energy. The original laws of thermodynamics were conceived by observing large-scale properties of systems and with no understanding of the underlying atomic structure. The kinetic theory of gases developed in the mid-19th century. In general, the temperature of a body is a measure of its internal energy. The three existing laws are now calculated using statistics and quantum mechanics. The first law of thermodynamics, basically a restatement of the conservation law of energy, is that the change in a system's internal energy is equal to the heat that flows into the system plus the work done on the system. The two main forms of change are adiabatic (without heat entering or leaving a system) and isothermal (at constant temperature). The second law says that if a system is left alone, its entropy tends to increase. This rules out the possibility of perpetual motion. The third law states that a system at absolute zero would effectively have an entropy of zero. See also Carnot cycle; Clausius; Kelvin

ther·mo·dy·nam·ics / ˌ[unvoicedth]ərmōdīˈnamiks/ • pl. n. [treated as sing.] the branch of physical science that deals with the relations between heat and other forms of energy (such as mechanical, electrical, or chemical energy), and, by extension, of the relationships and interconvertibility of all forms of energy. DERIVATIVES: ther·mo·dy·nam·ic adj. ther·mo·dy·nam·i·cal / -ikəl/ adj. ther·mo·dy·nam·i·cal·ly / -ik(ə)lē/ adv. ther·mo·dy·nam·i·cist / -ˌdīˈnamisist/ n.