The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system, and expresses the law of conservation of energy. Heat flowing from hot water to cold water 7.2 Derivation for systems described by the canonical ensemble.7.1 Derivation of the entropy change for reversible processes.7 Derivation from statistical mechanics.4.1 The second law in chemical thermodynamics.3.1 Perpetual motion of the second kind.2.10 Statement for a system that has a known expression of its internal energy as a function of its extensive state variables.2.6 Relation between Kelvin's statement and Planck's proposition.2.4 Equivalence of the Clausius and the Kelvin statements.The second law of thermodynamics can also be used to define the concept of thermodynamic temperature, but this is usually delegated to the zeroth law of thermodynamics. The first rigorous definition of the second law based on the concept of entropy came from German scientist Rudolph Clausius in the 1850s including 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. Its first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, credited to 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 second law has been expressed in many ways. Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules. Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. An increase in entropy accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. If all processes in the system are reversible, the entropy is constant.
The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest at the given internal energy. Entropy change predicts the direction of spontaneous processes, and determines whether they are irreversible or impossible despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system.
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