Since the Carnot principle, of the first part, is considered to be true for systems in thermodynamic equilibrium, these difficulties can be overcome by assuming that the Carnot principle is an independent fundamental law, without the need of demonstration. However, the derivation is not free from difficulties and, in fact, it has been criticized on the grounds that the reasonings and the hidden assumptions employed in the derivation are not totally clear E.H. Usually, both the first and the second part of the second law are derived from the Clausius or Kelvin statements of the second law. If the second law of thermodynamics is understood as a law about systems undergoing nonequilibrium processes, than only the second part should properly be identified as the second law. The second part, on the other hand, refers to systems that are not in equilibrium. The first aspect that comes to mind regarding the two parts is that the first part concerns systems that are in thermodynamic equilibrium, or more precisely systems that are undergoing an equilibrium process. Some are equivalent to the statements of Clausius and Kelvin, some are equivalent to the first part only, and some are equivalent to the second part only. In addition to the statements of Clausius and Kelvin, several other statements of the second law have appeared. The second part comprises the law of increase in entropy. The first part includes the Carnot principle, which states that all engines operating according to the Carnot cycle with the same temperatures have the same efficiency, and its main consequence that the ratio dQ/T of the infinitesimal heat and the temperature is an exact differential, which allows the definition of entropy. called the first and second parts of the second law. Sommerfeld, Thermodynamics and Statistical Mechanics (Academic Press, New York, 1956). can be understood as having two parts, which Sommerfeld A. Thomson, Transactions of the Royal Society of Edinburgh 20, 261 (1853). Clausius, Annalen der Physik und Chemie 79, 368, 500 (1850). The second law of thermodynamics as conceived by Clausius R.
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