Clausius and the Second Law of Thermodynamics
Rudolf Clausius was a pivotal figure in the development of thermodynamics, particularly known for his formulation of the second law of thermodynamics. This law states that heat naturally flows from hotter bodies to colder ones, establishing a fundamental principle that no process can occur that contradicts this trend. Clausius's work replaced the earlier caloric theory of heat and provided a quantitative measure of disorder in systems through the concept of entropy, which he introduced in 1865. This measure indicates that as energy transformations occur, disorder tends to increase, leading to the conclusion that useful energy is not fully conserved in processes. Clausius's insights have significant implications, affecting the efficiency of various systems, including engines and refrigerators, and they raise philosophical questions about the future of the universe, suggesting a "heat death" scenario. His contributions laid the groundwork for modern thermodynamics, influencing fields from engineering to biology. Understanding Clausius's second law is crucial for applications in energy conversion and the design of technology, making it a foundational concept in both science and practical energy management.
Clausius and the Second Law of Thermodynamics
Date 1850-1865
Rudolf Clausius’s second law of thermodynamics states that entropy in a system tends to increase. Along with his insights into the first law of thermodynamics, Clausius’s formulation of the second law established the foundation for modern thermodynamics. It also had profound effects upon the nineteenth century imagination, because it predicted the “heat death” of the universe.
Locale Germany
Key Figures
Rudolf Clausius (1822-1888), German physicist and mathematicianSadi Carnot (1796-1832), French physicistÉmile Clapeyron (1799-1864), French engineerPierre-Simon Laplace (1749-1827), French physicist and mathematicianSiméon-Denis Poisson (1781-1840), French physicist and mathematicianJames Prescott Joule (1818-1889), British physicistJulius Robert von Mayer (1814-1878), German physician and physicistHermann von Helmholtz (1821-1894), German physicistBaron Kelvin (William Thomson; 1824-1907), Scottish physicist and mathematicianLudwig Eduard Boltzmann (1844-1906), Austrian physicist
Summary of Event
While yet a young man, Rudolf Clausius developed the ability to think clearly, organize ideas, and see through the confusion that typically accompanies difficult problems. After entering the University of Berlin in 1840, Clausius decided to pursue a degree in physics and mathematics. In 1848, he earned his doctorate in physics from the University of Halle and became interested in the mechanical theory of heat. The 1840’s were a time of great interest in thermodynamics, the study of the relationship between heat and other forms of energy. Around 1842, James Prescott Joule and Julius Robert von Mayer had discovered the first law of thermodynamics, or conservation of energy, which was confirmed by Hermann von Helmholtz in 1847. In 1850, Clausius published a paper in Annalen der Physik (annals of physics) that analyzed the relationship between heat, work, and other thermodynamic variables.
Prior to the appearance of Clausius’s paper in 1850, the theory of heat, known as the caloric theory, was based on two fundamental premises: The heat in the universe is conserved, and the heat in a material depends on the state of that material. Pierre-Simon Laplace , Siméon-Denis Poisson, Sadi Carnot , and Émile Clapeyron had all developed thermodynamic concepts and relationships that were based upon the assumptions of the caloric theory.
By reformulating the first law of thermodynamics using the concept of the internal energy of a system, Clausius showed in his 1850 paper that both assumptions of the caloric theory were incorrect. He stated additionally that the natural tendency is for heat to flow from hot bodies to cold bodies and not the reverse. This was the first published statement of what became known as the second law of thermodynamics. Although the idea seems rather obvious for heat flow that occurs through the process of conduction, the principle stated by Clausius goes much further, asserting that no process whatever can occur that is in conflict with the second law. His 1850 paper was monumental in the development of thermodynamics. It replaced the caloric theory of heat with the first and second laws of thermodynamics, laying the foundation for modern thermodynamics.
Between 1850 and 1865, Clausius published an additional eight papers that applied and clarified the second law of thermodynamics. One of his first applications was to the efficiency of a heat engine. A heat engine is any device that absorbs heat from a higher temperature source, or reservoir, converts part of that energy into useful work, and dumps the rest to a lower temperature reservoir. Steam engines are a prime example. In 1824, Carnot had derived an equation for the efficiency of a simple heat engine based strictly on the first law of thermodynamics. In the 1850’s, Clausius determined the restrictions on the efficiency of a heat engine by also invoking the second law in the calculation of efficiency. He showed that the upper limit to the thermal efficiency of any heat engine is always less than one. He concluded that it is impossible to construct any device that will produce no effect other than the transfer of heat from a colder to a hotter body when it operates through a complete cycle. The consequence is that heat energy cannot be converted completely into mechanical energy by any heat engine.
Through his applications of the second law to heat engines and other thermodynamic systems, Clausius deduced that processes in nature are irreversible, always proceeding in a certain direction. This phenomenon is analogous to time only moving forward and not in reverse. Since it is impossible for a heat engine or any other system completely to convert the heat that it absorbs into mechanical work, the system cannot return to the same state in which it began. Clausius concluded that, since a system irrevocably lost some of its potential energy whenever it converted that energy from heat to work, the disorder of that system and its surroundings increased in the process. In a heat engine, for example, the particles that constitute the system are initially sorted into hotter and colder regions of space. This sorting, or ordering, is lost when the system performs work and thermal equilibrium is established.
Since the key word in the first law of thermodynamics was “energy,” Clausius wanted to find a similar word to characterize the second law. He settled on the word “entropy,” which originates from a Greek word meaning transformation and which he coined in a paper published in 1865. The word describes the increasing disorder endemic to natural processes. Clausius determined an equation that related entropy to heat and temperature. He then used entropy as a quantitative measure to determine the disorder or randomness of a system. In his 1865 paper, he restated the second law of thermodynamics in essentially the following form: the entropy of a system interacting with its surroundings always increases.
As revealed in the second law of thermodynamics, then, every event that occurs in the world results in a net increase in entropy. Although energy is conserved, useful energy is not, and an increase in entropy means a reduction in the ordered energy available for doing work in the future. The second law of thermodynamics is of utmost importance, since it imposes practical restrictions on the design and operation of numerous important systems, including gasoline and diesel engines in motorized vehicles, jet engines in airplanes, steam turbines in electric power plants, refrigerators, air conditioners, heat pumps, and the human body.
Significance
Since energy conversion is an essential aspect of human technology and of all plant and animal life, thermodynamics is of fundamental importance in the world. The work of Clausius in formulating the second law of thermodynamics laid the framework for modern thermodynamics. The practical significance of his formulation of the second law was recognized on several occasions during his lifetime. He was elected to the Royal Society of London in 1868 and received the Huygens Medal in 1870, the Copley Medal in 1879, and the Poncelet Prize in 1883. Baron Kelvin , who was also instrumental in the development of thermodynamics, pointed out that the principles of heat engines were first correctly established by applying Clausius’s second law of thermodynamics and his statement of the first law of thermodynamics. The contributions of Clausius to thermodynamics also formed the basis for future interpretations of the second law of thermodynamics by Ludwig Eduard Boltzmann and others in terms of probability, which led to the development of the field of statistical mechanics.
Several scientific discoveries of the nineteenth century had philosophical implications that questioned the place of humanity in the universe. The scandal caused by Charles Darwin’s theory of evolution, which seemed to question the biblical theory of Creation, is still well known today. Less remembered is the similar crisis caused by the second law of thermodynamics. Before Clausius’s discovery, the universe could, in theory, be eternal. The second law of thermodynamics, however, suggested that the universe must someday end: It predicted what came to be referred to as the “heat death” of the universe.
The fields of modern thermodynamics and statistical mechanics, which evolved from the work of Clausius and other prominent scientists, provide immense insight into how the everyday world works, with applications to engineering, biology, meteorology, electronics, and many other disciplines. The operation of engines and the limits on their efficiencies, the operation of refrigerators and the limits on their coefficients of performance and energy efficiency ratings (EER), the function of semiconductors in solid-state circuits as a function of temperature, and the analytical aspects of the human body operating as a thermodynamic engine or fuel cell are all based upon Clausius’s formulation of the second law of thermodynamics and his statement of the first law of thermodynamics. Energy-conversion research and the development of alternative energy resources, including solar energy systems, biomass systems, and nuclear power plants, are also dependent upon an understanding and application of Clausius’s insights into thermodynamic processes and the fundamental laws that govern them.
Bibliography
Cardwell, D. S. L. From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age. Ithaca, N.Y.: Cornell University Press, 1971. Provides details of the development of the laws of thermodynamics and the corresponding advancements in power technology.
Caton, Jerald A. A Review of Investigations Using the Second Law of Thermodynamics to Study Internal-Combustion Engines. London: Society of Automotive Engineers, 2000. Discusses applications of the second law of thermodynamics to determine the efficiency and operating restrictions associated with automobile engines.
Cole, K.C. The Universe and the Teacup: The Mathematics of Truth and Beauty. Fort Washington, Pa.: Harvest Books, 1999. Cole translates the mathematical complexities of the second law of thermodynamics into practical applications associated with engines and refrigerators.
Sandler, Stanley I. Chemical and Engineering Thermodynamics. New York: John Wiley & Sons, 1998. Reviews Clausius’s contributions to the second law of thermodynamics and its applications to chemical engineering.
Trefil, James, and Robert M. Hazen. The Sciences: An Integrated Approach. New York: John Wiley & Sons, 2003. Presents Clausius’s version of the second law, as well as alternative statements and practical applications of the law.