# Laws of thermodynamics

The four laws of thermodynamics define fundamental physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems. The laws describe how these quantities behave under various circumstances, and forbid certain phenomena (such as perpetual motion).

The four laws of thermodynamics are:[1][2][3][4][5][6]

• Zeroth law of thermodynamics: The zeroth law in its wider sense establishes a notion of internal thermodynamic equilibrium of a system.[7] In a narrow sense, the law states that if two systems are both in thermal equilibrium with a third system then they are in thermal equilibrium with each other. This law helps define the notion of temperature.
• Second law of thermodynamics: An isolated physical system, if not already in its own internal state of thermodynamic equilibrium, spontaneously evolves towards it. In an isolated physical system, there is a tendency towards spatial homogeneity. In particular, when an isolated physical system reaches its own internal state of thermodynamic equilibrium, its temperature is spatially uniform. When work is done on or by a thermodynamic system, a certain amount of that energy is lost to inefficiency, related to the difference between the energy level of the input and the output. This loss is described by the notion of entropy, which is often used to express the law. Some of the loss is due to friction when work is done, and some of it may be due to the relaxation of the system towards spatial homogeneity. The law says that these two mechanisms occur always and inevitably. The law implies that perpetual motion machines of the second kind are impossible.
• Third law of thermodynamics: There are various ways of expressing the third law.[8] They derive from the statistical mechanical explanation of thermodynamics. They refer to ideally perfect theoretical models of physical systems. A common expression of the law states that no practicable means can bring a physical system to an exactly zero absolute thermodynamic temperature.

Classical thermodynamics describes the exchange of work and heat between closed systems. It has a special interest in systems that are individually in states of thermodynamic equilibrium. 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 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,[9] 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.[1][2][3][4][5][10][11]

The laws of thermodynamics are important fundamental laws in physics and they are applicable in other natural sciences.

## Zeroth law

The zeroth law of thermodynamics may be stated in the following form:

If two systems are both in thermal equilibrium with a third then they are in thermal equilibrium with each other.[1]

The law is intended to allow the existence of an empirical parameter, the temperature, as a property of a system such that systems in thermal equilibrium with each other have the same temperature. The law as stated here is compatible with the use of a particular physical body, for example a mass of gas, to match temperatures of other bodies, but does not justify regarding temperature as a quantity that can be measured on a scale of real numbers.

Though this version of the law is one of the more commonly stated, it is only one of a diversity of statements that are labeled as "the zeroth law" by competent writers. Some statements go further so as to supply the important physical fact that temperature is one-dimensional, that one can conceptually arrange bodies in real number sequence from colder to hotter.[12][13][14] Perhaps there exists no unique "best possible statement" of the "zeroth law", because there is in the literature a range of formulations of the principles of thermodynamics, each of which call for their respectively appropriate versions of the law.

Although these concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century, the desire to explicitly number the above law was not widely felt until Fowler and Guggenheim did so 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. Such a temperature definition is said to be 'empirical'.[15][16][17][18][19][20]

## First law

The first law of thermodynamics may be stated in several ways:

The increase in internal energy of a body is equal to the heat supplied to the body minus work done by the body.
For a thermodynamic cycle, the heat supplied to a closed system, minus that removed from it, equals the net work done by the system.
The increase in internal energy of a closed system for any process of interest between an initial and a final state of internal thermodynamic equilibrium is equal to the change in internal energy for a reference process consisting only of adiabatic work that goes from that initial to that final state.

More specifically, the First Law encompasses several principles:

This states that energy can be neither created nor destroyed. However, energy can change forms, and energy can flow from one place to another. The total energy of an isolated system remains the same.
If a system has a definite temperature, then its total energy has three distinguishable components. If it is in motion, it has kinetic energy. If it is in an externally imposed force field (e.g. gravity), it has potential energy. And it has internal energy which is the sum of the kinetic energy of microscopic motions of its constituent atoms, and of the potential energy of interactions between them. Other things being equal, the kinetic energy of microscopic motions of the constituent atoms increases as the system's temperature increases. The establishment of the concept of internal energy is the characteristic distinguishing feature of the first law of thermodynamics.
• The flow of heat is a form of energy transfer.
In other words, a quantity of heat that flows from a hot body to a cold one can be expressed as an amount of energy being transferred from the hot body to the cold one.
• Performing work is a form of energy transfer.
For example, when a machine lifts a heavy object upwards, some energy is transferred from the machine to the object. The object acquires its energy in the form of gravitational potential energy in this example.
• When matter is transferred, energy is transferred with it.

Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a perpetual motion machine which will continuously do work without consuming energy.

## Second law

The second law of thermodynamics asserts the irreversibility of natural processes, and the tendency of natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature. It can be formulated in a variety of interesting and important ways.

It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that

When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium in itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables equal; then the final system also has the same values.

This statement of the law recognizes that in classical thermodynamics, the entropy of a system is defined only when it has reached its own internal thermodynamic equilibrium.

The second law refers to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a convenient theoretical fiction and do not occur in nature.

A 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 initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.

The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.

According to the second law of thermodynamics, in a theoretical and fictional reversible heat transfer, an element of heat transferred, δQ, is the product of the temperature (T), both of the system and of the sources or destination of the heat, with the increment (dS) of the system's conjugate variable, its entropy (S)

$\delta Q = T\,dS\, .$[1]

Entropy may also be viewed as a physical measure of the lack of physical information about the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. The law asserts that for two given macroscopically specified states of a system, there is a quantity called the difference of information entropy between them. This information entropy difference defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other - often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. 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 increase tells how much extra microscopic information is needed to distinguish the final macroscopically specified state from the initial macroscopically specified state.[21]

## Third law

The third law of thermodynamics is sometimes stated as follows:

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy. Entropy is related to the number of possible microstates according to S = kBln(Ω), where S is the entropy of the system, kB Boltzmann's constant, and Ω the number of microstates (e.g. possible configurations of atoms). At absolute zero there is only 1 microstate possible (Ω=1) and ln(1) = 0.

A more general form of the third law that applies to a systems such as a glass that may have more than one minimum microscopically distinct energy state, or may have a microscopically distinct state that is "frozen in" though not a strictly minimum energy state and not strictly speaking a state of thermodynamic equilibrium, at absolute zero temperature:

The entropy of a system approaches a constant value as the temperature approaches zero.

The constant value (not necessarily zero) is called the residual entropy of the system.

## History

Count Rumford (born Benjamin Thompson) showed, about 1797, that endless mechanical action can generate indefinitely large amounts of heat from a fixed amount of working substance, so challenging the caloric theory that held that there would be a finite amount of caloric in a fixed amount of working substance. The historically first established thermodynamic principle which eventually became the second law of thermodynamics was formulated by Sadi Carnot during 1824. By 1860, as formalized in the works of those such as Rudolf Clausius and William Thomson, 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, 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.

## Jocular mnemonic

Chemist and novelist C. P. Snow once remarked that not knowing the second law of thermodynamics was "like having never read a work by Shakespeare."[22] The following simple expression of the four laws has been attributed to Snow:[23]

• Zeroth law: You must play the game
• First law: You can't win
• Second law: You can't break even
• Third law: You can't quit the game.

## References

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2. ^ a b Kittel, C. Kroemer, H. (1980). Thermal Physics, second edition, W.H. Freeman, San Francisco, ISBN 0-7167-1088-9.
3. ^ a b Adkins, C.J. (1968). Equilibrium Thermodynamics, McGraw-Hill, London, ISBN 0-07-084057-1.
4. ^ a b Kondepudi D. (2008). Introduction to Modern Thermodynamics, Wiley, Chichester, ISBN 978-0-470-01598-8.
5. ^ a b Lebon, G., Jou, D., Casas-Vázquez, J. (2008). Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers, Springer, Berlin, ISBN 978-3-540-74252-4.
6. ^ Chris Vuille; Serway, Raymond A.; Faughn, Jerry S. (2009). College physics. Belmont, CA: Brooks/Cole, Cengage Learning. p. 355. ISBN 0-495-38693-6.
7. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 20.
8. ^ Guggenheim, E.A. (1985). Thermodynamics. An Advanced Treatment for Chemists and Physicists, seventh edition, North Holland, Amsterdam, ISBN 0-444-86951-4, p. 59.
9. ^ Balescu, R. (1975). Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York, ISBN 0-471-04600-0.
10. ^ De Groot, S.R., Mazur, P. (1962). Non-equilibrium Thermodynamics, North Holland, Amsterdam.
11. ^ Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley-Interscience, London, ISBN 0-471-30280-5.
12. ^ Sommerfeld, A. (1951/1955). Thermodynamics and Statistical Mechanics, vol. 5 of Lectures on Theoretical Physics, edited by F. Bopp, J. Meixner, translated by J. Kestin, Academic Press, New York, page 1.
13. ^ Serrin, J. (1978). The concepts of thermodynamics, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janiero, August 1977, edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, ISBN 0-444-85166-6, pages 411-451.
14. ^ Serrin, J. (1986). Chapter 1, 'An Outline of Thermodynamical Structure', pages 3-32, in New Perspectives in Thermodynamics, edited by J. Serrin, Springer, Berlin, ISBN 3-540-15931-2.
15. ^ Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, (first edition 1968), third edition 1983, Cambridge University Press, ISBN 0-521-25445-0, pp. 18–20.
16. ^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 26.
17. ^ Buchdahl, H.A. (1966), The Concepts of Classical Thermodynamics, Cambridge University Press, London, pp. 30, 34ff, 46f, 83.
18. ^ *Münster, A. (1970), Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London, ISBN 0-471-62430-6, p. 22.
19. ^ Pippard, A.B. (1957/1966). Elements of Classical Thermodynamics for Advanced Students of Physics, original publication 1957, reprint 1966, Cambridge University Press, Cambridge UK, p. 10.
20. ^ Wilson, H.A. (1966). Thermodynamics and Statistical Mechanics, Cambridge University Press, London UK, pp. 4, 8, 68, 86, 97, 311.
21. ^ Ben-Naim, A. (2008). A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific, New Jersey, ISBN 978-981-270-706-2.
22. ^ Atkins, Peter (2007). Four Laws That Drive the Universe. Oxford University Press. ISBN 9780191647635.
23. ^ Mahon, Tom (2011). Reconnecting.calm. ISBN 9780983724100.