Kinetic theory of gases
The kinetic theory of gases describes a gas as a large number of submicroscopic particles, all of which are in constant, random motion. The randomness arises from the particles' many collisions with each other and with the walls of the container. Kinetic theory of gases explains the macroscopic properties of gases, such as pressure, viscosity, thermal conductivity, volume, by considering their molecular composition and motion; the theory posits that gas pressure results from particles' collisions with the walls of a container at different velocities. Kinetic molecular theory defines temperature in its own way, in contrast with the thermodynamic definition. Under an optical microscope, the molecules making up a liquid are too small to be visible. However, the jittery motion of pollen grains or dust particles in liquid are visible. Known as Brownian motion, the motion of the pollen or dust results from their collisions with the liquid's molecules. In 50 BCE, the Roman philosopher Lucretius proposed that static macroscopic bodies were composed on a small scale of moving atoms all bouncing off each other.
This Epicurean atomistic point of view was considered in the subsequent centuries, when Aristotlean ideas were dominant. In 1738 Daniel Bernoulli published Hydrodynamica, which laid the basis for the kinetic theory of gases. In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, that what we experience as heat is the kinetic energy of their motion. Bernoulli surmised that temperature was the effect of the kinetic energy of the molecules, thus correlated with the ideal gas law; the theory was not accepted, in part because conservation of energy had not yet been established, it was not obvious to physicists how the collisions between molecules could be elastic. A competing theory favored by Newton was the replussion theory, in which heat was a calorific fluid that repulsed molecules in proportion its quantity and the inverse square of the distances between molecules.
Other pioneers of the kinetic theory were Mikhail Lomonosov, Georges-Louis Le Sage, John Herapath and John James Waterston, which connected their research with the development of mechanical explanations of gravitation. In 1856 August Krönig created a simple gas-kinetic model, which only considered the translational motion of the particles. In 1857 Rudolf Clausius, according to his own words independently of Krönig, developed a similar, but much more sophisticated version of the theory which included translational and contrary to Krönig rotational and vibrational molecular motions. In this same work he introduced the concept of mean free path of a particle. In 1859, after reading a paper on the diffusion of molecules by Rudolf Clausius, Scottish physicist James Clerk Maxwell formulated the Maxwell distribution of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range; this was the first-ever statistical law in physics. Maxwell gave the first mechanical argument that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium.
In his 1873 thirteen page article'Molecules', Maxwell states: "we are told that an'atom' is a material point and surrounded by'potential forces' and that when'flying molecules' strike against a solid body in constant succession it causes what is called pressure of air and other gases." In 1871, Ludwig Boltzmann generalized Maxwell's achievement and formulated the Maxwell–Boltzmann distribution. The logarithmic connection between entropy and probability was first stated by him. In the beginning of the twentieth century, atoms were considered by many physicists to be purely hypothetical constructs, rather than real objects. An important turning point was Albert Einstein's and Marian Smoluchowski's papers on Brownian motion, which succeeded in making certain accurate quantitative predictions based on the kinetic theory; the theory for ideal gases makes the following assumptions: The gas consists of small particles known as molecules. This smallness of their size is such that the total volume of the individual gas molecules added up is negligible compared to the volume of the smallest open ball containing all the molecules.
This is equivalent to stating that the average distance separating the gas particles is large compared to their size. These particles have the same mass; the number of molecules is so large. The moving particles collide among themselves and with the walls of the container. All these collisions are elastic; this means the molecules are considered to be spherical in shape and elastic in nature. Except during collisions, the interactions among molecules are negligible; this implies: 1. Relativistic effects are negligible. 2. Quantum-mechanical effects are negligible; this means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules are treated as classical objects. 3. Because of the above two, their dynamics can be treated classically; this means. The average kinetic energy of the gas particles depends only on the absolute temperature of the system; the kinetic theory has its own definition of temperature, not identical with the thermodynamic definition. The elapsed time of a co
James Clerk Maxwell
James Clerk Maxwell was a Scottish scientist in the field of mathematical physics. His most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the "second great unification in physics" after the first one realised by Isaac Newton. With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. Maxwell proposed that light is an undulation in the same medium, the cause of electric and magnetic phenomena; the unification of light and electrical phenomena led to the prediction of the existence of radio waves. Maxwell helped develop the Maxwell–Boltzmann distribution, a statistical means of describing aspects of the kinetic theory of gases, he is known for presenting the first durable colour photograph in 1861 and for his foundational work on analysing the rigidity of rod-and-joint frameworks like those in many bridges.
His discoveries helped usher in the era of modern physics, laying the foundation for such fields as special relativity and quantum mechanics. Many physicists regard Maxwell as the 19th-century scientist having the greatest influence on 20th-century physics, his contributions to the science are considered by many to be of the same magnitude as those of Isaac Newton and Albert Einstein. In the millennium poll—a survey of the 100 most prominent physicists—Maxwell was voted the third greatest physicist of all time, behind only Newton and Einstein. On the centenary of Maxwell's birthday, Einstein described Maxwell's work as the "most profound and the most fruitful that physics has experienced since the time of Newton". James Clerk Maxwell was born on 13 June 1831 at 14 India Street, Edinburgh, to John Clerk Maxwell of Middlebie, an advocate, Frances Cay daughter of Robert Hodshon Cay and sister of John Cay, his father was a man of comfortable means of the Clerk family of Penicuik, holders of the baronetcy of Clerk of Penicuik.
His father's brother was the 6th Baronet. He had been born "John Clerk", adding Maxwell to his own after he inherited the Middlebie estate, a Maxwell property in Dumfriesshire. James was a first cousin of both the artist Jemima Blackburn and the civil engineer William Dyce Cay. Cay and Maxwell were close friends and Cay acted as his best man when Maxwell married. Maxwell's parents married when they were well into their thirties, they had had one earlier child, a daughter named Elizabeth. When Maxwell was young his family moved to Glenlair, in Kirkcudbrightshire which his parents had built on the estate which comprised 1,500 acres. All indications suggest. By the age of three, everything that moved, shone, or made a noise drew the question: "what's the go o' that?" In a passage added to a letter from his father to his sister-in-law Jane Cay in 1834, his mother described this innate sense of inquisitiveness: He is a happy man, has improved much since the weather got moderate. He investigates the hidden course of streams and bell-wires, the way the water gets from the pond through the wall....
Recognising the potential of the young boy, Maxwell's mother Frances took responsibility for James's early education, which in the Victorian era was the job of the woman of the house. At eight he could recite the whole of the 119th psalm. Indeed, his knowledge of scripture was detailed, his mother was taken ill with abdominal cancer and, after an unsuccessful operation, died in December 1839 when he was eight years old. His education was overseen by his father and his father's sister-in-law Jane, both of whom played pivotal roles in his life, his formal schooling began unsuccessfully under the guidance of a 16 year old hired tutor. Little is known about the young man hired to instruct Maxwell, except that he treated the younger boy harshly, chiding him for being slow and wayward; the tutor was dismissed in November 1841 and, after considerable thought, Maxwell was sent to the prestigious Edinburgh Academy. He lodged during term times at the house of his aunt Isabella. During this time his passion for drawing was encouraged by his older cousin Jemima.
The 10 year old Maxwell, having been raised in isolation on his father's countryside estate, did not fit in well at school. The first year had been full, obliging him to join the second year with classmates a year his senior, his mannerisms and Galloway accent struck the other boys as rustic. Having arrived on his first day of school wearing a pair of homemade shoes and a tunic, he earned the unkind nickname of "Daftie", he never seemed bearing it without complaint for many years. Social isolation at the Academy ended when he met Lewis Campbell and Peter Guthrie Tait, two boys of a similar age who were to become notable scholars in life, they remained lifelong friends. Maxwell was fascinated by geometry at an early age, rediscovering the regular polyhedra before he received any formal instruction. Despite winning the school's scripture biography prize in his second year, his academic work remained unnoticed until, at the
Physics is the natural science that studies matter, its motion, behavior through space and time, that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy the oldest. Over much of the past two millennia, chemistry and certain branches of mathematics, were a part of natural philosophy, but during the scientific revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, the boundaries of physics which are not rigidly defined. New ideas in physics explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics enable advances in new technologies.
For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have transformed modern-day society, such as television, domestic appliances, nuclear weapons. Astronomy is one of the oldest natural sciences. Early civilizations dating back to beyond 3000 BCE, such as the Sumerians, ancient Egyptians, the Indus Valley Civilization, had a predictive knowledge and a basic understanding of the motions of the Sun and stars; the stars and planets were worshipped, believed to represent gods. While the explanations for the observed positions of the stars were unscientific and lacking in evidence, these early observations laid the foundation for astronomy, as the stars were found to traverse great circles across the sky, which however did not explain the positions of the planets. According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, all Western efforts in the exact sciences are descended from late Babylonian astronomy.
Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey. Natural philosophy has its origins in Greece during the Archaic period, when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause, they proposed ideas verified by reason and observation, many of their hypotheses proved successful in experiment. The Western Roman Empire fell in the fifth century, this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, continued to advance various fields of learning, including physics. In the sixth century Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. In sixth century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noting its flaws.
He introduced the theory of impetus. Aristotle's physics was not scrutinized until John Philoponus appeared, unlike Aristotle who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics John Philoponus wrote: “But this is erroneous, our view may be corroborated by actual observation more than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as the other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a small one, and so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as the other”John Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries during the Scientific Revolution.
Galileo cited Philoponus in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus, it was a step toward the modern ideas of momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further placing emphasis on observation and a priori reasoning, developing early forms of the scientific method; the most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn al-Haytham, in which he conclusively disproved the ancient Greek idea about vision, but came up with a new theory. In the book, he presented a study of the phenomenon of the camera obscura (his thousand-year-old
ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.
Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.
This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.
Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.
Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev
Paul Ehrenfest was an Austrian and Dutch theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. Paul Ehrenfest grew up in Vienna in a Jewish family from Loštice in Moravia, his parents, Sigmund Ehrenfest and Johanna Jellinek, ran a grocery store. Although the family was not overly religious, Paul studied Hebrew and the history of the Jewish people, he always emphasized his Jewish roots. Ehrenfest excelled in grade school but did not do well at the Akademisches Gymnasium, his best subject being mathematics. After transferring to the Franz Josef Gymnasium, his marks improved. In 1899 he passed the final exams, he majored in chemistry at the Institute of technology, but took courses at the University of Vienna, in particular from Ludwig Boltzmann on his kinetic theory of thermodynamics. These lectures had a profound influence: they were instrumental in developing Ehrenfest's interest in theoretical physics, defined his main area of research for years to come, provided an example of inspired teaching.
At the time it was customary in the German-speaking world to study at more than one university and in 1901 Ehrenfest transferred to Göttingen, which until 1933 was an important centre for mathematics and theoretical physics. There he met his future wife Tatyana Afanasyeva, a young mathematician born in Kiev capital of the Kiev Governorate, Russian Empire, educated in St Petersburg. In the spring of 1903 he met H. A. Lorentz during a short trip to Leiden. In the meantime he prepared a dissertation on Die Bewegung starrer Körper in Flüssigkeiten und die Mechanik von Hertz, he obtained his Ph. D. degree on 23 June 1904 in Vienna, where he stayed from 1904 to 1905. On 21 December 1904 he married Russian mathematician Tatyana Alexeyevna Afanasyeva, who collaborated with him in his work, they had two daughters and two sons: Tatyana became a mathematician. The Ehrenfests returned to Göttingen in September 1906, they would not see Boltzmann again: on September 6 Boltzmann took his own life in Duino near Trieste.
Ehrenfest published an extensive obituary in which Boltzmann's accomplishments are described. Felix Klein, dean of the Göttinger mathematicians and chief editor of the Enzyklopädie der mathematischen Wissenschaften, had counted on Boltzmann for a review about statistical mechanics. Now he asked Ehrenfest to take on this task. Together with his wife, Ehrenfest worked on it for several years, it is a review of the work of Boltzmann and his school, shows a style all of its own: a sharp logical analysis of the fundamental hypotheses, clear delineation of unsolved questions, an explanation of general principles by cleverly chosen transparent examples. In 1907 the couple moved to St Petersburg. Ehrenfest found good friends there, in particular A. F. felt scientifically isolated. Moreover, as an Austrian citizen and of Jewish origin, he had no prospect of a permanent position. Early in 1912 Ehrenfest set out on a tour of German-speaking universities in the hope of a position, he visited Berlin where he saw Max Planck, Leipzig where he saw his old friend Herglotz, Munich where he met Arnold Sommerfeld Zürich and Vienna.
While in Prague he met Albert Einstein for the first time, they remained close friends thereafter. Einstein recommended Ehrenfest to succeed him in his position in Prague; this was due to the fact. Sommerfeld offered him a position in Munich. H. A. Lorentz resigned his position as professor at the University of Leiden, on his advice Ehrenfest was appointed as his successor. In October 1912 Ehrenfest arrived in Leiden, on 4 December he gave his inaugural lecture Zur Krise der Lichtaether-Hypothese, he remained in Leiden for the rest of his career. In order to stimulate interaction and exchange among physics students he organized a discussion group and a study association called De Leidsche Flesch, he maintained close contact with prominent physicists within the country and abroad, invited them to visit to Leiden and give a presentation in his lecture series. Ehrenfest was an outstanding debater, quick to summarize the essentials. In his lectures he would focus on simple models and examples to illustrate and clarify the underlying assumptions.
His classes were small, he made an effort to get to know students who made use of the reading room. Though few of them were accepted as majors in Theoretical Physics, he had long discussions with them on a daily basis. According to Einstein: He was not the best teacher in our profession whom I have known. To understand others, to gain their friendship and trust, to aid anyone embroiled in outer or inner struggles, to encourage youthful talent—all this was his real element more than his immersion in scientific problems. If Ehrenfest felt that there was little more he could teach his students, he would send them to other centers in Europe for more training, he would encourage them to accept positions abroad. Among his students were Johannes Burgers, Hendrik Kramers, Dirk Coster, George Uhlenbeck