Equivalence of First and Second Laws
Building on Carnot’s foundation for the determination of motive power in steam engines, Clausius introduced two functions of state and built around them the first and second law of thermodynamics. Perhaps due to his desire to formulate a “mechanical theory of heat,” he constructed the first law as a generalization of the conservation of energy in mechanics, resulting in the definition of the internal energy, and allowed for violations in the definition of the entropy as a function of state to be the indicators of the irreversibility of what Clausius termed “uncompensated transformations.” In this chapter, we will show that Clausius’s choice is, to a large extent, a matter of taste: The entropy function can be preserved, and violations in the internal energy can determine the “ordering of states” when less than maximum work is performed by the engine.
We can say that Carnot knew the second law, but was ignorant of the first law. This is why he had to introduce his general and special axioms in order to determine the work done. In contrast, Clausius knew the first law, but allowed for violations in the second law to accommodate the possibility of wasted heat given off to the cold reservoir. Whereas both formulations attribute an increase in heat rejected to the cold reservoir as the origin of irreversibility, or the wasted portion of work that the engine was capable of doing, they do so in different ways. By reformulating Carnot’s general and special axioms, it will be possible to obtain an analytical expression for this wasted heat, whereas Clausius can only derive an inequality for his “uncompensated” transformations.
KeywordsElectromotive Force Maximum Work Steam Engine Heat Uptake Carnot Cycle
Unable to display preview. Download preview PDF.