ABSTRACT
Concepts of reservoirs and Perpetual Motion Machines of the second kind (PMM2) are introduced. Kelvin-Plank’s statement of the second law of a PMM2 being impossible and Clausius’ statement of the impossibility of spontaneous heat transfer from a cold to a hot reservoir are shown to be equivalent. The Carnot principle of reversible engines having higher efficiencies than irreversible engines and all reversible engines having the same efficiencies when operating between the same set of reservoirs are derived. The reversible heat transfer from a reservoir operating a reversible engine is proportional to the absolute temperature of the reservoir. This absolute temperature defines the thermodynamic temperature. For a cyclic system doing work, the Clausius inequality specifies the sum of the ratios of heat transfer between the system and the reservoirs to the absolute temperature of the reservoirs to be less than or equal to zero. The inequality is shown to follow the second law. When the heat transfer between the cyclic system and the reservoirs is reversible, the above sum is zero and hence defines a path-independent property called as entropy. The second law is stated in terms of entropy change in an isolated system, and this definition is shown to be equivalent to the statements of Kelvin-Plank and Clausius.
