INTRODUCTION
Thermodynamics, 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 isolable 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.
II.
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.)
Temperatures are measured with devices called thermometers (see Thermometer). A
thermometer contains a substance with conveniently identifiable and reproducible states, such as
the normal boiling and freezing points of pure water. If a graduated scale is marked between two
such states, the temperature of any system can be determined by having that system brought into
thermal contact with the thermometer, provided that the system is large relative to the
thermometer.
III.
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 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 × 107 ergs, or 4.186 joules.
The first law, then, is a law of energy conservation. It states that, because energy cannot be
created or destroyed—setting aside the later ramifications of the equivalence of mass and energy
(see Nuclear 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.
IV.
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.
V.
THERMODYNAMIC
CYCLES
Carnot Engine
Carnot Engine
The idealized Carnot engine was envisioned by the French physicist Nicolas Léonard Sadi
Carnot, who lived during the early 19th century. The Carnot engine is theoretically perfect,
that is, it converts the maximum amount of energy into mechanical work. Carnot showed
that the efficiency of any engine depends on the difference between the highest and lowest
temperatures reached during one cycle. The greater the difference, the greater the
efficiency. An automobile engine, for example, would be more efficient if the fuel burned
hotter and the exhaust gas came out of the cylinder at a lower temperature.
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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—that is, all the heat
would be converted to mechanical work. The 19th-century French scientist Nicolas Léonard 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 Carnot
cycle.
VI.
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.
VII.
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 of entropy 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.