Laws of thermodynamics

# Laws of thermodynamics

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The four laws of thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

summarize its most important facts. They define fundamental physical quantities, such as temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

, and entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

, in order to describe thermodynamic system
Thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....

s. They also describe the transfer of energy as heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

and work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

in thermodynamic processes
Thermodynamic processes
A thermodynamic process may be defined as the energetic development of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant...

. The experimentally reproducible distinction between heat and work is at the heart of thermodynamics; thermodynamics has nothing to say about processes in which this distinction cannot be made.

The four principles, or laws, of thermodynamics are:
• The zeroth law of thermodynamics
Zeroth law of thermodynamics
The zeroth law of thermodynamics is a generalization principle of thermal equilibrium among bodies, or thermodynamic systems, in contact.The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.Systems are said to...

recognizes that if two systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other, thus supporting the notions of temperature and heat.

• The first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

distinguishes between two kinds of physical process, namely energy transfer as work, and energy transfer as heat. It tells how this shows the existence of a mathematical quantity called the internal energy of a system. The internal energy obeys the principle of conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

but work and heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

are not defined as separately conserved quantities. Equivalently, the first law of thermodynamics states that perpetual motion machines of the first kind are impossible.

• The second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

distinguishes between reversible and irreversible physical processes. It tells how this shows the existence of a mathematical quantity called the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

of a system, and thus it expresses the irreversibility of actual physical processes by the statement that the entropy of an isolated macroscopic system never decreases. Equivalently, perpetual motion machines of the second kind are impossible.

• The third law of thermodynamics
Third law of thermodynamics
The third law of thermodynamics is a statistical law of nature regarding entropy:For other materials, the residual entropy is not necessarily zero, although it is always zero for a perfect crystal in which there is only one possible ground state.-History:...

concerns the entropy of a perfect crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

at absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....

temperature, and implies that it is impossible to cool a system to exactly absolute zero, or, equivalently, that perpetual motion machines of the third kind are impossible.

Classical thermodynamics describes the exchange of work and heat between systems. It has a special interest in systems that are individually in states of thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

. Thermodynamic equilibrium is a condition of systems which are adequately described by only macroscopic variables. Every physical system, however, when microscopically examined, shows apparently random microscopic statistical fluctuations
Fluctuation theorem
The fluctuation theorem , which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium will increase or decrease over a given amount of time...

in its thermodynamic variables of state (entropy, temperature, pressure, etc.). These microscopic fluctuations are negligible for systems which are nearly in thermodynamic equilibrium and which are only macroscopically examined. They become important, however, for systems which are nearly in thermodynamic equilibrium when they are microscopically examined, and, exceptionally, for macroscopically examined systems that are in critical states, and for macroscopically examined systems that are far from thermodynamic equilibrium.

There have been suggestions of additional laws, but none of them achieve the generality of the four accepted laws, and they are not mentioned in standard textbooks.

The laws of thermodynamics are important fundamental law
Physical law
A physical law or scientific law is "a theoretical principle deduced from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present." Physical laws are typically conclusions...

s in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

and they are applicable in other natural sciences.

## Zeroth law

The zeroth law of thermodynamics
Zeroth law of thermodynamics
The zeroth law of thermodynamics is a generalization principle of thermal equilibrium among bodies, or thermodynamic systems, in contact.The zeroth law states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.Systems are said to...

may be stated as follows:
The zeroth law implies that thermal equilibrium, viewed as a binary relation
Binary relation
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...

, is a Euclidean relation
Euclidean relation
In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's "Common Notion 1" in The Elements: things which equal the same thing also equal one another.-Definition:...

. If we assume that the binary relationship is also reflexive
Reflexive relation
In mathematics, a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation ~ on S where x~x holds true for every x in S. For example, ~ could be "is equal to".-Related terms:...

, then it follows that thermal equilibrium is an equivalence relation
Equivalence relation
In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition. Two elements of the set are considered equivalent if and only if they are elements of the same cell...

. Equivalence relations are also transitive
Transitive relation
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....

and symmetric
Symmetric relation
In mathematics, a binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.In mathematical notation, this is:...

. The symmetric relationship allows one to speak of two systems being "in thermal equilibrium with each other", which gives rise to a simpler statement of the zeroth law:
However, this statement requires the implicit assumption of both symmetry and reflexivity, rather than reflexivity alone.

The law is also a statement about measurability. To this effect the law allows the establishment of an empirical parameter, the temperature, as a property of a system such that systems in equilibrium with each other have the same temperature. The notion of transitivity permits a system, for example a gas thermometer, to be used as a device to measure the temperature of another system.

Although the concept of thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

is fundamental to thermodynamics, the need to state it explicitly as a law was not widely perceived until Fowler and Planck stated it in the 1930s, long after the first, second, and third law were already widely understood and recognized. Hence it was numbered the zeroth law. The importance of the law as a foundation to the earlier laws is that it allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable.

## First law

The first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

may be expressed by several forms of the fundamental thermodynamic relation:
Increase in internal energy of a system = heat supplied to the system + work done on the system.

For a thermodynamic cycle
Thermodynamic cycle
A thermodynamic cycle consists of a series of thermodynamic processes transferring heat and work, while varying pressure, temperature, and other state variables, eventually returning a system to its initial state...

, the net heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

supplied to the system equals the net work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

done by the system.

The net change in internal energy is the energy that flows in as heat minus the energy that flows out as the work that the system performs on its environment. Work and heat are not defined as separately conserved quantities; they refer only to processes of exchange of energy.

These statements entail that the internal energy obeys the principle of conservation of energy. The principle of conservation of energy may be stated in several ways:

## Second law

The second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

asserts the existence of a quantity called the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

of a system and further states that
It follows that the entropy of an isolated macroscopic system never decreases. The second law states that spontaneous natural processes increase entropy overall, or in another formulation that heat can spontaneously be conducted or radiated only from a higher-temperature region to a lower-temperature region, but not the other way around.

The second law refers to a wide variety of processes, reversible and irreversible. Its main import is to tell about irreversibility.

The prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies of different temperatures are connected with each other by purely thermal connection, conductive or radiative, then heat always flows from the hotter body to the colder one. This fact is part of the basic idea of heat, and is related also to the so-called zeroth law, though the textbooks' statements of the zeroth law are usually reticent about that, because they have been influenced by Carathéodory's basing his axiomatics on the law of conservation of energy and trying to make heat seem a theoretically derivative concept instead of an axiomatically accepted one. Šilahvý (1997) notes that Carathéodory's approach does not work for the description of irreversible processes that involve both heat conduction and conversion of kinetic energy into internal energy by viscosity (which is another prime example of irreversibility), because "the mechanical power and the rate of heating are not expressible as differential forms in the 'external parameters'".

The second law tells also about kinds of irreversibility other than heat transfer, and the notion of entropy is needed to provide that wider scope of the law.

According to the second law of thermodynamics, in a reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the source or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

(S)

The second law defines entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

, which may be viewed not only as a macroscopic variable of classical thermodynamics, but may also be viewed as a measure of deficiency of physical information about the microscopic details of the motion and configuration of the system, given only predictable experimental reproducibility of bulk or macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...

behavior as specified by macroscopic variables that allow the distinction to be made between heat and work. More exactly, the law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of entropy between them. The entropy difference tells how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other, which is often a conveniently chosen reference state. It is often convenient to presuppose the reference state and not to explicitly state it. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes. The entropy increase tells how much extra microscopic information is needed to tell the final macroscopically specified state from the initial macroscopically specified state.

## Third law

The third law of thermodynamics
Third law of thermodynamics
The third law of thermodynamics is a statistical law of nature regarding entropy:For other materials, the residual entropy is not necessarily zero, although it is always zero for a perfect crystal in which there is only one possible ground state.-History:...

is usually stated as follows:

This is explained in statistical mechanics by the fact that a perfect crystal has only one possible microstate
Microstate (statistical mechanics)
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations...

(microscopic state) at extremely low temperatures: The locations and energies of every atom in a crystal are known and fixed. (In quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, the location of each atom is not exactly fixed, but the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

of each atom is fixed in the unique ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...

for its position in the crystal.) Entropy is related to the number of possible microstates, and with only one microstate, the entropy is exactly zero.

The third law is also stated in a form that includes non-crystal systems, such as glass
Glass
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...

es:

The minimum, not necessarily zero, is called the residual entropy
Residual entropy
Residual entropy is small amount of entropy which is present even after a substance is cooled arbitrarily close to absolute zero. It occurs if a material can exist in many different microscopic states when cooled to absolute zero...

of the system.

## History

In about 1797, Count Rumford (born Benjamin Thompson) showed
Mechanical equivalent of heat
In the history of science, the mechanical equivalent of heat was a concept that had an important part in the development and acceptance of the conservation of energy and the establishment of the science of thermodynamics in the 19th century....

that mechanical action can generate indefinitely large amounts of heat, so challenging the caloric theory. The historically first established thermodynamic principle which eventually became the second law of thermodynamics was formulated by Sadi Carnot
Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

during 1824. By 1860, as formalized in the works of those such as Rudolf Clausius
Rudolf Clausius
Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...

and William Thomson
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

, two established principles of thermodynamics had evolved, the first principle and the second principle, later restated as thermodynamic laws. By 1873, for example, thermodynamicist Josiah Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

, in his memoir Graphical Methods in the Thermodynamics of Fluids, clearly stated the first two absolute laws of thermodynamics. Some textbooks throughout the 20th century have numbered the laws differently. In some fields removed from chemistry, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Directly defining zero points for entropy calculations was not considered to be a law. Gradually, this separation was combined into the second law and the modern third law was widely adopted.

• Conservation law
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

• Heat death of the universe
Heat death of the universe
The heat death of the universe is a suggested ultimate fate of the universe, in which the universe has diminished to a state of no thermodynamic free energy and therefore can no longer sustain motion or life. Heat death does not imply any particular absolute temperature; it only requires that...

• Laws of science
• Table of thermodynamic equations
Table of thermodynamic equations
The following page is a concise list of common thermodynamic equations and quantities:-Entropy:*~ S = k_B ~, where k_B is the Boltzmann constant, and \Omega denotes the volume of macrostate in the phase space....

• Ginsberg's Theorem
Ginsberg's Theorem
Ginsberg's theorem is a set of adages which restate the laws of thermodynamics in terms of a person playing a game. The quote is attributed to the poet Allen Ginsberg.-Theorem:...