Systematic treatment of the second law

Much of the preliminary discussion above has been lacking in precision. However, aU that we require for a systematic treatment of the second law is the fact, which is securely based on experience, that it is impossible to carry out Joule s experiment in reverse (Statement A below). As a postulate, to be justified later, we shall also assume the existence of reversible paths. On this basis the development of the second law may be carried out in several different ways. In the following we shall describe the traditional method, as used by dausiuef and Poincar, which depends on the use of heat engines. The main alternatives are the methods of Planck, which depends on the existence of perfect gases, and of Bom and Carathto-dory, II which is based on the properties of Pfaffian differential expressions. 

II Bom, Phys. Z, 22 (1921), 218, 249, 282. An excellent account in Ehiglish is given by Chandrasekhar, Introduction to the Study of Stellar Structure (Dover, 1957). Versions of the Carath4odory treatment are also given by Buchdahl, The Concepts of Classical Thermodynamics (Cambridge, 1966) Bom, Natural Philosophy of Cause and Chance (Oxford, 1949) Eisenschitz, Science Progress, 43 (1955), 246 Turner, Amer. J. Phys. 28 (1960), 781 29 (1961), 40 Thomson, ibid. 29 (1961), 300 Sears, ibid. 31 (1963), 747 and Munster, Classical Thermodynamics (Wiley-Interscience, 1970). 

Statement A. It is impossible to make a transfer of heat from a heat bath, at a uniform temperature, and obtain an equivalent amount of work, without causing a change in the therrnodynamic state of some other body. 

Some comments on the phrasing of this statement may to added. 

Statement A will now be used to prove the following four propositions  

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