|Three of the more famous cyclical processes of thermodynamics: the Carnot cycle, showing isotherms and adiabatic curves, the Clapeyron cycle, showing isochores and isotherms, and the Clausius-Rankine cycle, showing adiabatic curves and isobars, each showing the changes of stage of the body on pressure-volume diagrams. |
The essential example, as visualized in the concept of "re-establishment of equilibrium in the caloric" as described by French physicist Sadi Carnot in his 1824 Reflections on the Motive Power of Fire, being that in which a body of gas, enclosed in cylinder and piston, at a specific pressure and volume, is expanded, due to the input of heat, and then contracted, due to the removal of heat, back to its original position (and assumed molecular arrangement) quantified by the values of the original pressure and volume.
The integral of an indefinitely "small change" in internal energy is given by the following expression:
each signifying, respectively, the initial and final values of the sums of the heat contents H and ergal contents J of the body.
For a cyclical process, according to German physicist Rudolf Clausius, the integral of the change in internal energy is zero, being that initial and final conditions of the body are assumed, by definition, to be the same, or U1 equals U2. 
The following are related quotes:
“A conception not reducible to the small change of daily experience is like a currency not exchangeable for articles of consumption; it is not a symbol, but a fraud.”— George Santayana (1906), “Reason in Society” 
1. Clausius, Rudolf. (1879). The Mechanical Theory of Heat (pg. 33). London: Macmillan & Co.
2. (a) Santayana, George. (1906). The Life of Reason (§8: Reason in Society) (Ѻ) Publisher.
(b) Andrews, Robert. (1993). The Columbia Dictionary of Quotations (pg. 906). Columbia University Press.
3. Author. (1979). The Great Soviet Encyclopedia (Ѻ). Publisher.
● Cyclic process – TheFreeDictionary.com.