Engineering Thermodynamics And The Carnot Cycle

The Carnot cycle is central to engineering thermodynamics and its teaching. Although on the one hand it is an unattainable ideal, on the other it constitutes a set of concepts to which real heat engine cycles and processes should aspire to and approximate. The Two Property Rule means that cycles may be represented graphically and the principal pairs of properties are p, v (pressure and specific volume) and T,s (temperature and specific entropy). The p, v diagram is truly practical in the sense that it mirrors the indicator diagram, known to generations of past engineering students from engine laboratory experiments. The indicator and its diagram have a venerable history, dating back to 1796 and the very dawn of thermodynamics. The Scotsman James Watt used them to improve engine design to considerable commercial advantage. In 1824, Carnot was unaware of the diagram, most probably because of its extreme commercial sensitivity for Watt. Not until 1834 did Clapeyron make the first use of the p, v diagram to describe the Carnot cycle. The T,s diagram was proposed by the American J (Josiah) Willard Gibbs in 1873 as part of a more general study of how graphical methods could be used in thermodynamics. Gibbs was a mathematical physicist and his thermodynamic contribution was almost a complete inverse to that of Watt. Despite it dating from well after the understanding of the Laws, the T,s diagram and the Carnot cycle are virtually indistinguishable in present-day understanding. So in representing Sadi Carnot’s cycle of 1824 with both p, v and T,s diagrams (which he was unable to do) almost a century of associated thermodynamics history is involved. In this chapter, we study the historical context of these diagrams and their authors. In particular, James Watt was a massive contributor to the industrial revolution and in certain respects a forerunner to Carnot. We use these diagrams to show how the Carnot concept of a perfect heat engine applies across the thermodynamic board, irrespective of working fluid (gas or vapour), of cycle processes (non-flow or steady flow) or of engine concept (work-producer or refrigerator). In addition, the Carnot cycle was the driving force behind the formulation of the Second Law of Thermodynamics and this aspect is reviewed to highlight the contributions of Kelvin himself. We will find that Kelvin has an enduring high reputation here, based on his absolute scale of temperature and his second law statement.