John Dalton FRS was an English chemist and meteorologist. He is best known for his work in the development of modern atomic theory and his research into colour blindness. John Dalton was born into a Quaker family in Eaglesfield, near Cockermouth and he received his early education from his father and from Quaker John Fletcher, who ran a private school in the nearby village of Pardshaw Hall. With his family too poor to support him for long, he began to earn his living at the age of ten in the service of a wealthy local Quaker, Elihu Robinson. It is said he began teaching at a school at age 12. He joined his older brother Jonathan at age 15 in running a Quaker school in Kendal, around age 23 Dalton may have considered studying law or medicine, but his relatives did not encourage him, perhaps because being a Dissenter, he was barred from attending English universities. He acquired much scientific knowledge from informal instruction by John Gough, at age 27 he was appointed teacher of mathematics and natural philosophy at the New College in Manchester, a dissenting academy.
He remained there until age 34, when the colleges worsening financial situation led him to resign his post and begin a new career as a tutor for mathematics. During his years in Kendal, Dalton contributed solutions of problems and questions on subjects to The Ladies Diary. In 1787 at age 21 he began to keep a diary in which, during the succeeding 57 years. He rediscovered George Hadleys theory of atmospheric circulation around this time, Daltons first publication was Meteorological Observations and Essays at age 27 in 1793, which contained the seeds of several of his discoveries. However, in spite of the originality of his treatment, little attention was paid to them by other scholars, a second work by Dalton, Elements of English Grammar, was published at age 35 in 1801. In fact, a shortage of colour perception in people had not even been formally described or officially noticed until Dalton wrote about his own. Since both he and his brother were colour blind, he recognized that this condition must be hereditary, examination of his preserved eyeball in 1995 demonstrated that Dalton actually had a less common kind of colour blindness, deuteroanopia, in which medium wavelength sensitive cones are missing.
The altitude achieved was estimated using a barometer and this meant that, until the Ordnance Survey started publishing their maps for the Lake District in the 1860s, Dalton was one of the few sources of such information. Dalton was often accompanied by Jonathan Otley, who was one of the few other authorities on the heights of the Lake District mountains and he became both an assistant and a friend. These four essays were presented between 2 and 30 October 1801 and published in the Memoirs of the Literary and Philosophical Society of Manchester in 1802. It seems, that general laws respecting the absolute quantity and he thus enunciated Gay-Lussacs law, published in 1802 at age 36 by Joseph Louis Gay-Lussac
In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat in a solid. It treats the vibrations of the lattice as phonons in a box, in contrast to the Einstein model. The Debye model correctly predicts the low temperature dependence of the heat capacity, just like the Einstein model, it recovers the Dulong–Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures, see M. Shubin and T. Sunada for a rigorous treatment of the Debye model. The Debye model is an equivalent of Plancks law of black body radiation. The Debye model treats atomic vibrations as phonons in a box, most of the calculation steps are identical. Consider a cube of side L, from the particle in a box article, the resonating modes of the sonic disturbances inside the box have wavelengths given by λ n =2 L n, where n is an integer. The energy of a phonon is E n = h ν n, in three dimensions we will use, E n 2 = p n 2 c s 2 =2, in which p n is the magnitude of the three-dimensional momentum of the phonon.
Lets now compute the energy in the box, E = ∑ n E n N ¯. In other words, the energy is equal to the sum of energy multiplied by the number of phonons with that energy. In 3 dimensions we have, U = ∑ n x ∑ n y ∑ n z E n N ¯, this is where Debye model and Plancks law of black body radiation differ. Unlike electromagnetic radiation in a box, there is a number of phonon energy states because a phonon cannot have infinite frequency. Its frequency is bound by the medium of its propagation—the atomic lattice of the solid, consider an illustration of a transverse phonon below. It is reasonable to assume that the wavelength of a phonon is twice the atom separation. There are N atoms in a solid and our solid is a cube, which means there are N3 atoms per edge. Atom separation is given by L / N3, and this is the upper limit of the triple energy sum U = ∑ n x N3 ∑ n y N3 ∑ n z N3 E n N ¯. For slowly varying, well-behaved functions, a sum can be replaced with an integral U ≈ ∫0 N3 ∫0 N3 ∫0 N3 E N ¯ d n x d n y d n z.
So far, there has no mention of N ¯
Kinetic theory of gases
Kinetic theory explains macroscopic properties of gases, such as pressure, viscosity, thermal conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure is due to the impacts, on the walls of a container, Kinetic theory defines temperature in its own way, not identical with the thermodynamic definition. Under a microscope, the making up a liquid are too small to be visible. Known as Brownian motion, it directly from collisions between the grains or particles and liquid molecules. As analyzed by Albert Einstein in 1907, this evidence for kinetic theory is generally seen as having confirmed the concrete material existence of atoms. The theory for ideal gases makes the assumptions, The gas consists of very small particles known as molecules. This smallness of their size is such that the 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 distance separating the gas particles is large compared to their size.
These particles have the same mass, the number of molecules is so large that statistical treatment can be applied. These molecules are in constant and rapid motion, the rapidly moving particles constantly collide among themselves and with the walls of the container. All these collisions are perfectly elastic and this means, the molecules are considered to be perfectly spherical in shape, and elastic in nature. Except during collisions, the interactions among molecules are negligible and this means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules are treated as classical objects. Because of the two, their dynamics can be treated classically. This means that the equations of motion of the molecules are time-reversible, 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 collision between a molecule and the containers wall is negligible when compared to the time between successive collisions.
Because they have mass, the gas molecules will be affected by gravity, more modern developments relax these assumptions and are based on the Boltzmann equation. These can accurately describe the properties of gases, because they include the volume of the molecules. The necessary assumptions are the absence of quantum effects, molecular chaos, expansions to higher orders in the density are known as virial expansions
Kopps law can refer to either of two relationships discovered by the German chemist Hermann Franz Moritz Kopp. In studying organic compounds, Kopp found a relationship between boiling points and the number of CH2 groups present. Frederick Seitz, The Modern Theory of Solids, McGraw-Hill, New York, USA,1940, ASIN, B000OLCK08 Thorpe, the Life Work of Hermann Kopp. Memorial lectures delivered before the Chemical Society
A temperature is an objective comparative measurement of hot or cold. It is measured by a thermometer, several scales and units exist for measuring temperature, the most common being Celsius, and, especially in science, Kelvin. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, the kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. Temperature is important in all fields of science including physics, chemistry, atmospheric sciences, medicine. The Celsius scale is used for temperature measurements in most of the world. Because of the 100 degree interval, it is called a centigrade scale.15, the United States commonly uses the Fahrenheit scale, on which water freezes at 32°F and boils at 212°F at sea-level atmospheric pressure. Many scientific measurements use the Kelvin temperature scale, named in honor of the Scottish physicist who first defined it and it is a thermodynamic or absolute temperature scale.
Its zero point, 0K, is defined to coincide with the coldest physically-possible temperature and its degrees are defined through thermodynamics. The temperature of zero occurs at 0K = −273. 15°C. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, Temperature is one of the principal quantities in the study of thermodynamics. There is a variety of kinds of temperature scale and it may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century, empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a capillary tube, is dependent largely on temperature. Such scales are only within convenient ranges of temperature. For example, above the point of mercury, a mercury-in-glass thermometer is impracticable. A material is of no use as a thermometer near one of its phase-change temperatures, in spite of these restrictions, most generally used practical thermometers are of the empirically based kind.
Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and they rely on theoretical properties of idealized devices and materials
The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm.
When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 7002273160280000000♠0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 7003130000000000000♠1300 K.
In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 6977138065049999999♠1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 7003400000000000000♠4000 K appear reddish, whereas those above about 7003750000000000000♠7500 K appear bluish
Albert Einstein was a German-born theoretical physicist. He developed the theory of relativity, one of the two pillars of modern physics, Einsteins work is known for its influence on the philosophy of science. Einstein is best known in popular culture for his mass–energy equivalence formula E = mc2, near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led him to develop his theory of relativity during his time at the Swiss Patent Office in Bern. Briefly before, he aquired the Swiss citizenship in 1901, which he kept for his whole life and he continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He investigated the properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the theory of relativity to model the large-scale structure of the universe.
He was visiting the United States when Adolf Hitler came to power in 1933 and, being Jewish, did not go back to Germany and he settled in the United States, becoming an American citizen in 1940. This eventually led to what would become the Manhattan Project, Einstein supported defending the Allied forces, but generally denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955. Einstein published more than 300 scientific papers along with over 150 non-scientific works, on 5 December 2014, universities and archives announced the release of Einsteins papers, comprising more than 30,000 unique documents. Einsteins intellectual achievements and originality have made the word Einstein synonymous with genius, Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire, on 14 March 1879.
His parents were Hermann Einstein, a salesman and engineer, the Einsteins were non-observant Ashkenazi Jews, and Albert attended a Catholic elementary school in Munich from the age of 5 for three years. At the age of 8, he was transferred to the Luitpold Gymnasium, the loss forced the sale of the Munich factory. In search of business, the Einstein family moved to Italy, first to Milan, when the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to electrical engineering, but Einstein clashed with authorities and resented the schools regimen. He wrote that the spirit of learning and creative thought was lost in strict rote learning, at the end of December 1894, he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctors note. During his time in Italy he wrote an essay with the title On the Investigation of the State of the Ether in a Magnetic Field
Pierre Louis Dulong
Pierre Louis Dulong FRS FRSE IOF was a French physicist and chemist, remembered today largely for the law of Dulong and Petit. He worked on the heat capacity and the expansion and refractive indices of gases. Dulong was born in Rouen, France, an only child, he was orphaned at the age of 4, he was brought up by his aunt on Auxerre. He gained his education in Auxerre and the Lycée Pierre Corneille in Rouen before entering the École Polytechnique. He began studying medicine, but gave this up to concentrate on science, Dulong succeeded Alexis Thérèse Petit as professor of physics, from 1820 to 1829, was directeur des études until his death. In chemistry, he contributed to knowledge on, the decomposition of salts nitrous acid the oxides of phosphorus the oxides of nitrogen catalysis by metals. Dulong discovered the dangerously sensitive nitrogen trichloride in 1812, losing two fingers and an eye in the process, in 1820, he succeeded Petit as professor of physics at École Polytechnique. Dulong studied the elasticity of steam, the measurement of temperatures, and he made the first precise comparison of the mercury- and air-temperature scales.
In 1830, he was elected a member of the Royal Swedish Academy of Sciences. He died in Paris and his is one of the names of 72 scientists inscribed on the Eiffel Tower, at the time of his death, he was working on the development of precise methods in calorimetry. He is buried in Père Lachaise Cemetery and he was married to Emelie Augustine Riviere in 1803. Recherches sur quelques points de la Théorie de la Chaleur. Annales de Chimie et de Physique, english translation, Research on some important aspects of the theory of heat from Annals of Philosophy 14,189 –198. Chisholm, Hugh, ed. Dulong, Pierre Louis
In the Einstein model, each atom oscillates independently. The original theory proposed by Einstein in 1907 has great historical relevance, the heat capacity of solids as predicted by the empirical Dulong-Petit law was required by classical mechanics, the specific heat of solids should be independent of temperature. But experiments at low temperatures showed that the heat capacity changes, as the temperature goes up, the specific heat goes up until it approaches the Dulong and Petit prediction at high temperature. By employing Plancks quantization assumption, Einsteins theory accounted for the experimental trend for the first time. Together with the effect, this became one of the most important pieces of evidence for the need of quantization. Einstein used the levels of the mechanical oscillator many years before the advent of modern quantum mechanics. Einstein’s Theory of Specific Heats In Einsteins model, the specific heat approaches zero exponentially fast at low temperatures and this is because all the oscillations have one common frequency.
The correct behavior is found by quantizing the normal modes of the solid in the way that Einstein suggested. Then the frequencies of the waves are not all the same, and the specific heat goes to zero as a T3 power law and this modification is called the Debye Model, which appeared in 1912. When Walther Nernst learned of Einsteins 1907 paper on specific heat, he was so excited that he traveled all the way from Berlin to Zürich to meet with him. The heat capacity of an object at constant volume V is defined through the internal energy U as C V = V. T, to find the entropy consider a solid made of N atoms, each of which has 3 degrees of freedom. So there are 3 N quantum harmonic oscillators, next, we must compute the multiplicity of the system. That is, compute the number of ways to distribute q quanta of energy among N ′ SHOs, the number of arrangements of n objects is n. So the number of arrangements of q pebbles and N ′ −1 partitions is. However, if partition #3 and partition #5 trade places, no one would notice, the same argument goes for quanta.
To obtain the number of possible distinguishable arrangements one has to divide the number of arrangements by the number of indistinguishable arrangements. There are q. identical quanta arrangements, therefore, multiplicity of the system is given by Ω =. Q. which, as mentioned before, is the number of ways to deposit q quanta of energy into N ′ oscillators, entropy of the system has the form S / k = ln Ω = ln
Quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of an equilibrium point. Furthermore, it is one of the few quantum-mechanical systems for which an exact, the first term in the Hamiltonian represents the possible kinetic energy states of the particle, and the second term represents its corresponding possible potential energy states. One may solve the differential equation representing this eigenvalue problem in the basis, for the wave function ⟨x|ψ⟩ = ψ. It turns out there is a family of solutions. In this basis, they amount to ψ n =12 n n. ⋅1 /4 ⋅ e − m ω x 22 ℏ ⋅ H n, n =0,1,2, …. The functions Hn are the physicists Hermite polynomials, H n = n e z 2 d n d z n, the corresponding energy levels are E n = ℏ ω = ℏ2 ω. This energy spectrum is noteworthy for three reasons, the energies are quantized, meaning that only discrete energy values are possible, this is a general feature of quantum-mechanical systems when a particle is confined.
Second, these energy levels are equally spaced, unlike in the Bohr model of the atom. Third, the lowest achievable energy is not equal to the minimum of the well, but ħω/2 above it. This zero-point energy further has important implications in quantum field theory, as the energy increases, the probability density becomes concentrated at the classical turning points, where the states energy coincides with the potential energy. This is consistent with the harmonic oscillator, in which the particle spends most of its time at the turning points. The correspondence principle is thus satisfied, the ladder operator method, developed by Paul Dirac, allows extraction of the energy eigenvalues without directly solving the differential equation. It is generalizable to more complicated problems, notably in quantum field theory, the operator a is not Hermitian, since itself and its adjoint a† are not equal. The energy eigenstates |n⟩, when operated on by these ladder operators and it is evident that a†, in essence, appends a single quantum of energy to the oscillator, while a removes a quantum.
For this reason, they are referred to as creation and annihilation operators. From the relations above, we can define a number operator N. The commutation property yields N a † | n ⟩ = | n ⟩ = | n ⟩ = a † | n ⟩ and this means that a acts on |n⟩ to produce, up to a multiplicative constant, |n–1⟩, and a† acts on |n⟩ to produce |n+1⟩