The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into work in a cyclic process." These are informal definitions, however; more formal definitions appear below.
The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.
Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules. The second law has been expressed in many ways. Its first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that the efficiency of conversion of heat to work in a heat engine has an upper limit. The first rigorous definition of the second law based on the concept of entropy came from German scientist Rudolf Clausius in the 1850s and included his statement that heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.
The second law of thermodynamics allows the definition of the concept of thermodynamic temperature, but this has been formally delegated to the zeroth law of thermodynamics.
Introduction
The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system, and expresses its change for a closed system in terms of work and heat.Planck, M. (1897/1903), pp. 40–41. It can be linked to the law of conservation of energy.Munster A. (1970), pp. 8–9, 50–51. Conceptually, the first law describes the fundamental principle that systems do not consume or 'use up' energy, that energy is neither created nor destroyed, but is simply converted from one form to another.
The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense, and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings, that is, both the state of the system plus the state of its surroundings cannot be together, fully reversed, without implying the destruction of entropy.
For example, when a path for conduction or radiation is made available, heat always flows spontaneously from a hotter to a colder body. Such phenomena are accounted for in terms of entropy change.Planck, M. (1897/1903), pp. 79–107.Bailyn, M. (1994), Section 71, pp. 113–154. A heat pump can reverse this heat flow, but the reversal process and the original process, both cause entropy production, thereby increasing the entropy of the system's surroundings. If an isolated system containing distinct subsystems is held initially in internal thermodynamic equilibrium by internal partitioning by impermeable walls between the subsystems, and then some operation makes the walls more permeable, then the system spontaneously evolves to reach a final new internal thermodynamic equilibrium, and its total entropy, , increases.
In a reversible or quasi-static, idealized process of transfer of energy as heat to a closed thermodynamic system of interest, (which allows the entry or exit of energy – but not transfer of matter), from an auxiliary thermodynamic system, an infinitesimal increment () in the entropy of the system of interest is defined to result from an infinitesimal transfer of heat () to the system of interest, divided by the common thermodynamic temperature of the system of interest and the auxiliary thermodynamic system:Bailyn, M. (1994), p. 120.
Different notations are used for an infinitesimal amount of heat and infinitesimal change of entropy because entropy is a function of state, while heat, like work, is not.
For an actually possible infinitesimal process without exchange of mass with the surroundings, the second law requires that the increment in system entropy fulfills the inequality
This is because a general process for this case (no mass exchange between the system and its surroundings) may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature () and the temperature of the surroundings ().Adkins, C.J. (1968/1983), p. 75.
The equality still applies for pure heat flow (only heat flow, no change in chemical composition and mass),
which is the basis of the accurate determination of the absolute entropy of pure substances from measured heat capacity curves and entropy changes at phase transitions, i.e. by calorimetry.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).Principles of Modern Chemistry, Brooks Cole. p. 617.
The zeroth law of thermodynamics in its usual short statement allows recognition that two bodies in a relation of thermal equilibrium have the same temperature, especially that a test body has the same temperature as a reference thermometric body. For a body in thermal equilibrium with another, there are indefinitely many empirical temperature scales, in general respectively depending on the properties of a particular reference thermometric body. The second law allows a distinguished temperature scale, which defines an absolute, thermodynamic temperature, independent of the properties of any particular reference thermometric body.Zemansky, M.W. (1968), pp. 207–209.Quinn, T.J. (1983), p. 8.
Various statements of the law The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.
Carnot's principle The historical originCarnot, S. (1824/1986). of the second law of thermodynamics was in Sadi Carnot's theoretical analysis of the flow of heat in steam engines (1824). The centerpiece of that analysis, now known as a Carnot engine, is an ideal heat engine fictively operated in the limiting mode of extreme slowness known as quasi-static, so that the heat and work transfers are between subsystems that are always in their own internal states of thermodynamic equilibrium. It represents the theoretical maximum efficiency of a heat engine operating between any two given thermal or heat reservoirs at different temperatures. Carnot's principle was recognized by Carnot at a time when the caloric theory represented the dominant understanding of the nature of heat, before the recognition of the first law of thermodynamics, and before the mathematical expression of the concept of entropy. Interpreted in the light of the first law, Carnot's analysis is physically equivalent to the second law of thermodynamics, and remains valid today. Some samples from his book are:
In modern terms, Carnot's principle may be stated more precisely:
Clausius statement In 1850, the German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the Clausius statement: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.
The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.
Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat is transferred from cold to hot, but only when forced by an external agent, the refrigeration system.
Understanding the Clausius statement requires prior definition of the concepts of 'hot versus cold' (temperature) and 'heat' (heat interaction). Within the Gyftopoulos-Beretta formulation of the general principles of thermodynamics, where temperature and heat are defined after the definitions of energy and entropy, the Clausius statement emerges as a rigorous consequence (theorem) of the first law and the Hatsopoulos-Keenan statement of the second law (see below).
Kelvin statements Lord Kelvin expressed the second law in several wordings.
The Kelvin–Planck statement does not rule out the possibility of a system developing a net amount of work from a heat transfer drawn from a single reservoir. It only denies this possibility if the system undergoes a thermodynamic cycle.
Equivalence of the Clausius and the Kelvin statements
Suppose there is an engine violating the Kelvin statement: i.e., one that drains heat and converts it completely into work (the drained heat is fully converted to work) in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the right figure. The efficiency of a normal heat engine is η and so the efficiency of the reversed heat engine is 1/η. The net and sole effect of the combined pair of engines is to transfer heat from the cooler reservoir to the hotter one, which violates the Clausius statement. This is a consequence of the first law of thermodynamics, as for the total system's energy to remain the same; , so therefore , where (1) the sign convention of heat is used in which heat entering into (leaving from) an engine is positive (negative) and (2) is obtained by the definition of efficiency of the engine when the engine operation is not reversed. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.
Planck's proposition Planck offered the following proposition as derived directly from experience. This is sometimes regarded as his statement of the second law, but he regarded it as a starting point for the derivation of the second law.
Relation between Kelvin's statement and Planck's proposition