# Lars Onsager’s Discovery of Reciprocal Relations

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1968 Nobel Prize-

Lars Onsager was awarded the Nobel prize in 1968 for the discovery of reciprocal relations which are essential for non-equilibrium thermodynamics and irreversible processes. He was born in Kristiana, (which is now Oslo), Norway on November 27th, 1903. He attended the Norwegian Institute of Technology and graduated in 1925 as a chemical engineer. During this time, he specialized in physical chemistry and theoretical chemistry. [1]After graduating, he devoted his time to reforming and correcting the Debye-Huckle Theory. The original Debye-Huckle Theory is shown below.

Lars Onsager was not satisfied with this equation because it fails to properly analyze a strong electrolyte solutions. When in aqueous systems, these strong electrolytes produce ions. For example, in a salt and water solution, positive and negative ions are formed. Each electrical force an ion produces another ion is affected by it. Every ion is interacting with another in a solution, therefore, he needed to modify the equation to properly assess the thermodynamics in these electrolyte solutions. To analyze these solutions properly, he introduced a constant to account for the random ionic interaction. Onsager published his correction to the Debye-Huckle Theory in 1926. [2]The correction is shown below.

$\lambda$

=

(A+B

º) *

This correction could properly describe all electrolytes that become ions in a solution due to an added. These reciprocal relations of coefficients allow computation of a system that is in non-equilibrium thermodynamics.[3] It is now nicknamed the fourth law of thermodynamics. Once Lars Onsager published his correction, Peter Debye contacted Onsager to discuss the correction to his theory. Onsager traveled to Zurich, Germany to meet with Peter Debye in 1926. After their meeting, Debye was extremely impressed with Onsager and offered him a position as a assistant researcher at the Eidgenossische Technische Hochschule in Zurich, Germany. Peter Debye and Lars Onsager worked together until 1928. It was then that Lars Onsager was contacted by John’s Hopkins University and offered a position as a full-time professor. He moved from Germany to the United States to work at the university. Unfortunately, though, Lars Onsager was quickly let go. He was an extremely intelligent person, however, when teaching at an undergraduate level, he could not relay the information to the students in a more simplified manner. Instead, he was teaching undergraduate students Ph.D. level chemistry. In 1929, he was hired by Brown University as a graduate professor teaching statistical methods, but did not excel as an educator there as well, however, he was heavily focused on his research during this time. The research on irreversible thermodynamics he had conducted at Brown ultimately lead him to winning the Nobel prize. Unfortunately, though, Brown had to let Onsager go because he has virtually zero teaching ability and they could not afford to keep him employed as just a researcher. In 1933, Yale University offered him a position as a professor of theoretical chemistry and remained at Yale until 1945. [4]

Throughout his multiple careers from 1925-1945, he kept researching thermodynamics and in 1968 he was awarded the Nobel Prize on his work of irreversible thermodynamics. His Nobel prize winning research originally stemmed from the correction of the Debye-Huckle Theory. When he made the adjustment to the theory, he discovered that electrolytes in solution failed to obey symmetry laws. To correct for this, he found that the constants are reciprocally related. Therefore, an adjustment to the constants using variables would fix this. A similar concept applies in irreversible thermodynamics. Irreversible thermodynamics focuses on currents ions produce in systems. These currents are affected by factors such as heat. Heat can change the flow of the currents, the voltage, and the thermal conductivity. These currents can transport ions one way; however, they are not able to go back to the original state. Therefore, making the process irreversible. [5]

Onsager uses water as his prime example. He states that in water each molecule of H2O is surrounded by four more molecules of H2O. Each hydrogen is then next to two oxygen molecules. However, a hydrogen cannot be near or connected to two oxygen atoms at one time, therefore, there is a chance of rotation of the molecule due to bonding defects. H3O+ and OH is then produced. This Ionic mobility varies between temperatures. These bonding motilities are different in solid water, liquid water, or gaseous water. The mobility’s have been found to be highest in ice because it is a denser system. He measured the currents This mobilizes create non-constant currents in the molecule.[6] Onsager measured these currents by testing the forward and reverse voltages, which turned out to be nonequivalent. He proposed conducting an experiment on isotopic separation under applied heat simultaneously removing a mixture of high concentration. However, the experiment would require a platinum tube that would be four stories high. Brown University could not afford such a high cost experiment, so it could not be conducted. Instead, he started to avoid physical chemistry experiments and decided to focus on theoretical chemistry. Lars Onsager published his theory on these systems, but was quickly dismissed when he presented his ideas. These systems are shown below. [7]

Onsager knew his work was revolutionary and extremely vital to the scientific community but scientists were not fully accepting his work. It took Lars Onsager around thirty-seven years to be awarded for his Nobel prize winning work. After leaving Brown, almost ten years passed by before the work he conducted and published there was cited. It took until 1945, post-World War II it slowly became more and more popular. The experimental method he requested at Brown University involving the platinum tube for isotope separation was the same one used for the Manhattan Project. If Brown University had the funding, Lars Onsager would have been credited with the method of separating ions used for the separation of uranium ions for the atomic bomb. [8]

Lars Onsager impacted the scientific community tremendously. He figured out that there exist reciprocal relations between coefficients in fundamental equations for irreversible thermodynamic processes. These are essential to compute and measure accurately how these systems can work and how we can properly solve for them. In addition to this, these reciprocal relations can help us further understand biochemical systems in the human body. These systems contain electrolytes that ionize in water. These ions are constantly permeating membranes. This ionic transport can help us further understand which ions are being transported and which are not in the currents and if it we can further research medicinal value to this ionic behavior in a non-equilibrium system. [9] In addition, the field of molecular dynamics and hydrodynamics has expanded tremendously because of Lars Onsager. The theories Onsager worked on at Brown University can now be applied in building hydrodynamic equations that can properly describe a system of high electrolyte concentration. At Hong Kong University of Science and Technology, researchers are testing one and two component liquid-vapor flows, gels, viscous liquids, and liquid crystals and applying Onsager’s equation to test if it can help properly compute the interactions between ions in these different systems. [10] In addition, research involving ionic sensors, such as the one Onsager proposed to develop at Brown University and the one used for creating the atomic bomb, is growing. Using Onsager’s initial principles, the researchers at University of North Carolina and the University of Memphis are creating machines to further expand isotopic separation and electroanalytical measurements of ions. These tools help the researchers study single ion transfers, energies, and kinetic interaction on surfaces of systems that are irreversible. These machines can also be used to analyze electrolyte voltages, large polymers, and the transferability of ions in different liquids. By being able to analyze these systems in further detail, scientists can work toward creating synthetic membranes that could potentially allow passage and fluid movement in both directions of ionic currents in systems that are said to be irreversible[11]

Lars Onsager was an extraordinary human being with an extremely capable mind. From his time at Norwegian Institute of Technology, Eidgenossische Technische Hochschule, Johns Hopkins, Brown University, and Yale University, he never quit further researching his field of study even when people doubted his work. It took Lars Onsager thirty-seven years to be awarded for his Nobel prize winning work. However, he never quit what he was working on and could revolutionize chemistry as we know it. Lars Onsager died on October 5th, 1976, but his work is still extremely prominent and useful in the chemical and biochemical community today.

References

1. Buck, R. P.; Linder, E; The History of Ion Sensors. J. An. Chem., 2001, 1-12.
2. C; Claesson, S.; Onsager, L. Journal of Statistical Physics1998578(1), 1–20.
3. Eyink, G. L.; Sreenivasan, K. R.; Osager and the theory of hydrodynamic turbulence J. Am. Phy. Soc. 2006, 78, 87
4. Hemmer, P. C.; Hauge, E. H. Norwegian University of Science and Techology; Barry: Tronheim, Norway.1976
5. Onsager, L., Reciprocal relations in irreversible processes. Phys. Rev. 1931, 37, 405-26.
6. Onsager, L., Separation of gas (isotope) mixtures by irreversible processes. Phys. Rev. 1939, 55, 1136-7.
7. Onsager, L., Simultaneous irreversible processes. Beret. 18th Skand. Naturforskermode, Copenhagen 1929, 440-1.
8. The Nobel Prize in Chemistry 1968. https://www.nobelprize.org/prizes/chemistry/1968/onsager/biographical/ (accessed Apr 20, 2019)
9. Qian, T.; Xu, X.; Hydrodynamic boundary conditions derived from Onsager’s variation principle. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong 2017

1. [1] The Nobel Prize in Chemistry 1968. https://www.nobelprize.org/prizes/chemistry/1968/onsager/biographical/ (accessed Apr 20, 2019)
1. [2] Hemmer, P. C.; Hauge, E. H. Norwegian University of Science and Techology; Barry: Tronheim, Norway.1976
1. [3] Onsager, L., Reciprocal relations in irreversible processes. Phys. Rev. 1931, 37, 405-26.
1. [4] Hemmer, P. C.; Hauge, E. H. Norwegian University of Science and Techology; Barry: Tronheim, Norway.1976
1. [5] Onsager, L., Simultaneous irreversible processes. Beret. 18th Skand. Naturforskermode, Copenhagen 1929, 440-1.
1. [6] Eyink, G. L.; Sreenivasan, K. R.; Osager and the theory of hydrodynamic turbulence J. Am. Phy. Soc. 2006, 78, 87
1. [7] Buck, R. P.; Linder, E; The History of Ion Sensors. J. An. Chem., 2001, 1-12.
1. [8] Onsager, L., Separation of gas (isotope) mixtures by irreversible processes. Phys. Rev. 1939, 55, 1136-7.
1. C; Claesson, S.; Onsager, L. Journal of Statistical Physics1998578(1), 1–20.
1. [10] Qian, T.; Xu, X.; Hydrodynamic boundary conditions derived from Onsager’s variation principle. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong 2017
1. [11] C; Claesson, S.; Onsager, L. Journal of Statistical Physics1998578(1), 1–20.

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