Enthalpy, a property of a thermodynamic system, is equal to the system's internal energy plus the product of its pressure and volume. In a system enclosed so as to prevent matter transfer, for processes at constant pressure, the heat absorbed or released equals the change in enthalpy; the unit of measurement for enthalpy in the International System of Units is the joule. Other historical conventional units still in use include the calorie. Enthalpy comprises a system's internal energy, the energy required to create the system, plus the amount of work required to make room for it by displacing its environment and establishing its volume and pressure. Enthalpy is defined as a state function that depends only on the prevailing equilibrium state identified by the system's internal energy and volume, it is an extensive quantity. Enthalpy is the preferred expression of system energy changes in many chemical and physical measurements at constant pressure, because it simplifies the description of energy transfer.
In a system enclosed so as to prevent matter transfer, at constant pressure, the enthalpy change equals the energy transferred from the environment through heat transfer or work other than expansion work. The total enthalpy, H, of a system cannot be measured directly; the same situation exists in classical mechanics: only a change or difference in energy carries physical meaning. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; the ΔH is a positive change in endothermic reactions, negative in heat-releasing exothermic processes. For processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the pressure-volume work p ΔV done by the system on its surroundings; this means that the change in enthalpy under such conditions is the heat absorbed or released by the system through a chemical reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure refer to standard state: most 1 bar pressure.
Standard state does not speaking, specify a temperature, but expressions for enthalpy reference the standard heat of formation at 25 °C. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy and Gibbs energy. Real materials at common temperatures and pressures closely approximate this behavior, which simplifies enthalpy calculation and use in practical designs and analyses; the word enthalpy was coined late, in the early 20th century, in analogy with the 19th-century terms energy and entropy. Where energy uses the root of the Greek word ἔργον "work" to express the idea of "work-content" and where entropy uses the Greek word τροπή "transformation" to express the idea of "transformation-content", so by analogy, enthalpy uses the root of the Greek word θάλπος "warmth, heat" to express the idea of "heat-content"; the term does in fact stand in for the older term "heat content", a term, now deprecated as misleading, as dH refers to the amount of heat absorbed in a process at constant pressure only, but not in the general case.
Josiah Willard Gibbs used the term "a heat function for constant pressure" for clarity. Introduction of the concept of "heat content" H is associated with Benoît Paul Émile Clapeyron and Rudolf Clausius; the term enthalpy first appeared in print in 1909. It is attributed to Heike Kamerlingh Onnes, who most introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris, it gained currency only in the 1920s, notably with the Mollier Steam Tables and Diagrams, published in 1927. Until the 1920s, the symbol H was used, somewhat inconsistently, for "heat" in general; the definition of H as limited to enthalpy or "heat content at constant pressure" was formally proposed by Alfred W. Porter in 1922; the enthalpy of a thermodynamic system is defined as H = U + p V, where H is enthalpy U is the internal energy of the system p is pressure V is the volume of the systemEnthalpy is an extensive property. This means, it is convenient to introduce the specific enthalpy h = H m, where m is the mass of the system, or the molar enthalpy H m = H n, where n is the number of moles.
For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems: H = ∑ k H k, where H is the total enthalpy of all the subsystems k refers to the various subsystems H k refers to the enthalpy of each subsystem ∑ k
Ideal gas law
The ideal gas law called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations, it was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, Gay-Lussac's law. The ideal gas law is written as P V = n R T, where P, V and T are the pressure and absolute temperature, it is the same for all gases. It can be derived from the microscopic kinetic theory, as was achieved by August Krönig in 1856 and Rudolf Clausius in 1857; the state of an amount of gas is determined by its pressure and temperature. The modern form of the equation relates these in two main forms; the temperature used in the equation of state is an absolute temperature: the appropriate SI unit is the kelvin. The most introduced form is P V = n R T = N k B T, where: P is the pressure of the gas, V is the volume of the gas, n is the amount of substance of gas, N is the number of gas molecules, R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant, k B is the Boltzmann constant T is the absolute temperature of the gas.
In SI units, P is measured in pascals, V is measured in cubic metres, n is measured in moles, T in kelvins. R has the value 8.314 J/ ≈ 2 cal/, or 0.08206 L·atm/. How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful; the chemical amount is equal to total mass of the gas divided by the molar mass: n = m M. By replacing n with m/M and subsequently introducing density ρ = m/V, we get: P V = m M R T P = m V R T M P = ρ R M T Defining the specific gas constant Rspecific as the ratio R/M, P = ρ R specific T This form of the ideal gas law is useful because it links pressure and temperature in a unique formula independent of the quantity of the considered gas. Alternatively, the law may be written in terms of the specific volume v, the reciprocal of density, as P v = R specific T, it is common in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the universal gas constant is given a different symbol such as R ¯ to distinguish it.
In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to. In statistical mechanics the following molecular equation is derived from first principles P = n k B T, where P is the absolute pressure of the gas, n is the number of molecules in the given volume V, T is the absolute temperature, kB is the Boltzmann constant relating temperature and energy, given by: k B = R N A where NA is the Avogadro constant. From this we notice that for a gas of mass m, with an average particle mass of μ times the atomic mass constant, mu, the number of molecules will be given by N = m μ m u, since ρ = m/V = nμmu, we find that the ideal gas law can be rewritten as P = 1 V m μ m u k B T = k B μ m u ρ T. In SI units, P is measured in pascals, V in cubic metre
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure; some of these derive from a unit of force divided by a unit of area. Pressure may be expressed in terms of standard atmospheric pressure. Manometric units such as the centimetre of water, millimetre of mercury, inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer. Pressure is the amount of force applied at right angles to the surface of an object per unit area; the symbol for it is p or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is used; the usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, on writing style. Mathematically: p = F A, where: p is the pressure, F is the magnitude of the normal force, A is the area of the surface on contact.
Pressure is a scalar quantity. It relates the vector surface element with the normal force acting on it; the pressure is the scalar proportionality constant that relates the two normal vectors: d F n = − p d A = − p n d A. The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward; the equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect to say "the pressure is directed in such or such direction"; the pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same. Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point.
It is a fundamental parameter in thermodynamics, it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre; this name for the unit was added in 1971. Other units of pressure, such as pounds per square inch and bar, are in common use; the CGS unit of pressure is 0.1 Pa.. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre and the like without properly identifying the force units, but using the names kilogram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2. Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume, it is therefore related to energy density and may be expressed in units such as joules per cubic metre. Mathematically: p =; some meteorologists prefer the hectopascal for atmospheric air pressure, equivalent to the older unit millibar. Similar pressures are given in kilopascals in most other fields, where the hecto- prefix is used.
The inch of mercury is still used in the United States. Oceanographers measure underwater pressure in decibars because pressure in the ocean increases by one decibar per metre depth; the standard atmosphere is an established constant. It is equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa; because pressure is measured by its ability to displace a column of liquid in a manometer, pressures are expressed as a depth of a particular fluid. The most common choices are water; the pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column
Solid is one of the four fundamental states of matter. In solids particles are packed, it is characterized by structural resistance to changes of shape or volume. Unlike liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does; the atoms in a solid are bound to each other, either in a regular geometric lattice or irregularly. Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because in gases molecules are loosely packed; the branch of physics that deals with solids is called solid-state physics, is the main branch of condensed matter physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification and chemical composition; the atoms, molecules or ions that make up solids may be arranged in an orderly repeating pattern, or irregularly.
Materials whose constituents are arranged in a regular pattern are known as crystals. In some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Solid objects that are large enough to see and handle are composed of a single crystal, but instead are made of a large number of single crystals, known as crystallites, whose size can vary from a few nanometers to several meters; such materials are called polycrystalline. All common metals, many ceramics, are polycrystalline. In other materials, there is no long-range order in the position of the atoms; these solids are known as amorphous solids. Whether a solid is crystalline or amorphous depends on the material involved, the conditions in which it was formed. Solids that are formed by slow cooling will tend to be crystalline, while solids that are frozen are more to be amorphous; the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed.
While many common objects, such as an ice cube or a coin, are chemically identical throughout, many other common materials comprise a number of different substances packed together. For example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is a natural organic material consisting of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties; the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of ionic sodium and chlorine, which are held together by ionic bonds. In diamond or silicon, the atoms share form covalent bonds. In metals, electrons are shared in metallic bonding; some solids most organic compounds, are held together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding.
Metals are strong and good conductors of both electricity and heat. The bulk of the elements in the periodic table, those to the left of a diagonal line drawn from boron to polonium, are metals. Mixtures of two or more elements in which the major component is a metal are known as alloys. People have been using metals for a variety of purposes since prehistoric times; the strength and reliability of metals has led to their widespread use in construction of buildings and other structures, as well as in most vehicles, many appliances and tools, road signs and railroad tracks. Iron and aluminium are the two most used structural metals, they are the most abundant metals in the Earth's crust. Iron is most used in the form of an alloy, which contains up to 2.1% carbon, making it much harder than pure iron. Because metals are good conductors of electricity, they are valuable in electrical appliances and for carrying an electric current over long distances with little energy loss or dissipation. Thus, electrical power grids rely on metal cables to distribute electricity.
Home electrical systems, for example, are wired with copper for its good conducting properties and easy machinability. The high thermal conductivity of most metals makes them useful for stovetop cooking utensils; the study of metallic elements and their alloys makes up a significant portion of the fields of solid-state chemistry, materials science and engineering. Metallic solids are held together by a high density of shared, delocalized electrons, known as "metallic bonding". In a metal, atoms lose their outermost electrons, forming positive ions; the free electrons are spread over the entire solid, held together by electrostatic interactions between the ions and the electron cloud. The large number of free electrons gives metals their high values of electrical and thermal conductivity; the free electrons prevent transmission of visible light, making metals opaque and lustrous. More advanced models of metal properties consider the effect of the positive ions cores on the delocalised electrons.
As most metals have crystalline structure, those ions are arranged into a periodic lattice. Mathematically, the potential of the ion cores can be treated by various models, the simplest being the nearly free electron model. Minerals are
Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not occur until the 18th century; the 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data, it was not until after the elucidation of the laws of physics and more the development of the computer, allowing for the automated solution of a great many equations that model the weather, in the latter half of the 20th century that significant breakthroughs in weather forecasting were achieved. An important domain of weather forecasting is marine weather forecasting as it relates to maritime and coastal safety, in which weather effects include atmospheric interactions with large bodies of water. Meteorological phenomena are observable weather events that are explained by the science of meteorology.
Meteorological phenomena are described and quantified by the variables of Earth's atmosphere: temperature, air pressure, water vapour, mass flow, the variations and interactions of those variables, how they change over time. Different spatial scales are used to describe and predict weather on local and global levels. Meteorology, atmospheric physics, atmospheric chemistry are sub-disciplines of the atmospheric sciences. Meteorology and hydrology compose the interdisciplinary field of hydrometeorology; the interactions between Earth's atmosphere and its oceans are part of a coupled ocean-atmosphere system. Meteorology has application in many diverse fields such as the military, energy production, transport and construction; the word meteorology is from the Ancient Greek μετέωρος metéōros and -λογία -logia, meaning "the study of things high in the air". The ability to predict rains and floods based on annual cycles was evidently used by humans at least from the time of agricultural settlement if not earlier.
Early approaches to predicting weather were practiced by priests. Cuneiform inscriptions on Babylonian tablets included associations between rain; the Chaldeans differentiated 46 ° halos. Ancient Indian Upanishads contain mentions of seasons; the Samaveda mentions sacrifices to be performed. Varāhamihira's classical work Brihatsamhita, written about 500 AD, provides evidence of weather observation. In 350 BC, Aristotle wrote Meteorology. Aristotle is considered the founder of meteorology. One of the most impressive achievements described in the Meteorology is the description of what is now known as the hydrologic cycle; the book De Mundo noted If the flashing body is set on fire and rushes violently to the Earth it is called a thunderbolt. They are all called ` swooping bolts'. Lightning is sometimes smoky, is called'smoldering lightning". At other times, it travels in crooked lines, is called forked lightning; when it swoops down upon some object it is called'swooping lightning'. The Greek scientist Theophrastus compiled a book on weather forecasting, called the Book of Signs.
The work of Theophrastus remained a dominant influence in the study of weather and in weather forecasting for nearly 2,000 years. In 25 AD, Pomponius Mela, a geographer for the Roman Empire, formalized the climatic zone system. According to Toufic Fahd, around the 9th century, Al-Dinawari wrote the Kitab al-Nabat, in which he deals with the application of meteorology to agriculture during the Muslim Agricultural Revolution, he describes the meteorological character of the sky, the planets and constellations, the sun and moon, the lunar phases indicating seasons and rain, the anwa, atmospheric phenomena such as winds, lightning, floods, rivers, lakes. Early attempts at predicting weather were related to prophecy and divining, were sometimes based on astrological ideas. Admiral FitzRoy tried to separate scientific approaches from prophetic ones. Ptolemy wrote on the atmospheric refraction of light in the context of astronomical observations. In 1021, Alhazen showed that atmospheric refraction is responsible for twilight.
St. Albert the Great was the first to propose that each drop of falling rain had the form of a small sphere, that this form meant that the rainbow was produced by light interacting with each raindrop. Roger Bacon was the first to calculate the angular size of the rainbow, he stated. In the late 13th century and early 14th century, Kamāl al-Dīn al-Fārisī and Theodoric of Freiberg were the first to give the correct explanations for the primary rainbow phenomenon. Theoderic went further and explained the secondary rainbow. In 1716, Edmund Halley suggested that aurorae are caused by "magnetic effluvia" moving along the Earth's magnetic field lines. In 1441, King Sejong's son, Prince Munjong of Korea, invented the first standardized rain gauge; these were sent throughout the Joseon dynasty of Korea as an official tool to assess land taxes based
Properties of water
Water is a polar inorganic compound, at room temperature a tasteless and odorless liquid, nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "universal solvent" and the "solvent of life", it is the most abundant substance on Earth and the only common substance to exist as a solid and gas on Earth's surface. It is the third most abundant molecule in the universe. Water molecules form hydrogen bonds with each other and are polar; this polarity allows it to dissociate ions in salts and bond to other polar substances such as alcohols and acids, thus dissolving them. Its hydrogen bonding causes its many unique properties, such as having a solid form less dense than its liquid form, a high boiling point of 100 °C for its molar mass, a high heat capacity. Water is amphoteric, meaning that it can exhibit properties of an acid or a base, depending on the pH of the solution that it is in. Related to its amphoteric character, it undergoes self-ionization.
The product of the activities, or the concentrations of H+ and OH− is a constant, so their respective concentrations are inversely proportional to each other. Water is the chemical substance with chemical formula H2O. Water is a odorless liquid at ambient temperature and pressure. Liquid water has weak absorption bands at wavelengths of around 750 nm which cause it to appear to have a blue colour; this can be observed in a water-filled bath or wash-basin whose lining is white. Large ice crystals, as in glaciers appear blue. Unlike other analogous hydrides of the oxygen family, water is a liquid under standard conditions due to hydrogen bonding; the molecules of water are moving in relation to each other, the hydrogen bonds are continually breaking and reforming at timescales faster than 200 femtoseconds. However, these bonds are strong enough to create many of the peculiar properties of water, some of which make it integral to life. Within the Earth's atmosphere and surface, the liquid phase is the most common and is the form, denoted by the word "water".
The solid phase of water is known as ice and takes the structure of hard, amalgamated crystals, such as ice cubes, or loosely accumulated granular crystals, like snow. Aside from common hexagonal crystalline ice, other crystalline and amorphous phases of ice are known; the gaseous phase of water is known as water vapor. Visible steam and clouds are formed from minute droplets of water suspended in the air. Water forms a supercritical fluid; the critical temperature is 647 K and the critical pressure is 22.064 MPa. In nature this only occurs in hostile conditions. A example of occurring supercritical water is in the hottest parts of deep water hydrothermal vents, in which water is heated to the critical temperature by volcanic plumes and the critical pressure is caused by the weight of the ocean at the extreme depths where the vents are located; this pressure is reached at a depth of about 2200 meters: much less than the mean depth of the ocean. Water has a high specific heat capacity of 4.1814 J/ at 25 °C – the second highest among all the heteroatomic species, as well as a high heat of vaporization, both of which are a result of the extensive hydrogen bonding between its molecules.
These two unusual properties allow water to moderate Earth's climate by buffering large fluctuations in temperature. Most of the additional energy stored in the climate system since 1970 has accumulated in the oceans; the specific enthalpy of fusion of water is 333.55 kJ/kg at 0 °C: the same amount of energy is required to melt ice as to warm ice from −160 °C up to its melting point or to heat the same amount of water by about 80 °C. Of common substances, only that of ammonia is higher; this property confers resistance to melting on the ice of glaciers and drift ice. Before and since the advent of mechanical refrigeration, ice was and still is in common use for retarding food spoilage; the specific heat capacity of ice at −10 °C is 2.03 J/ and the heat capacity of steam at 100 °C is 2.08 J/. The density of water is about 1 gram per cubic centimetre: this relationship was used to define the gram; the density varies with temperature, but not linearly: as the temperature increases, the density rises to a peak at 3.98 °C and decreases.
This unusual negative thermal expansion below 4 °C is observed in molten silica. Regular, hexagonal ice is less dense than liquid water—upon freezing, the density of water decreases by about 9%. Other substances that expand on freezing are silicon, gallium (melting point of 303 K |, germanium and bismuth. Pure silicon has a negative coefficient of thermal expansion for temperatures between about 18 and 120 kelvins; these effects are due to the reduction of thermal motion with cooling, which allows water molecules to form more hydrogen bonds that prevent the molecules from coming close to each other. While below 4 °C the breakage of hydrogen bonds due to freezing allows water molecules to pack closer despite the increase in the thermal motion, above 4 °C water expands as the temperature increases. Water near the boiling point is ab
Rudolf Julius Emanuel Clausius was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he gave the theory of heat a truer and sounder basis, his most important paper, "On the Moving Force of Heat", published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem. Clausius was born in Köslin in the Province of Pomerania in Prussia, his father was a Protestant pastor and school inspector, Rudolf studied in the school of his father. After a few years, he went to the Gymnasium in Stettin. Clausius graduated from the University of Berlin in 1844 where he studied mathematics and physics with, among others, Gustav Magnus, Peter Gustav Lejeune Dirichlet and Jakob Steiner, he studied history with Leopold von Ranke. During 1847, he got his doctorate from the University of Halle on optical effects in Earth's atmosphere.
He became professor of physics at the Royal Artillery and Engineering School in Berlin and Privatdozent at the Berlin University. In 1855 he became professor at the ETH Zürich, the Swiss Federal Institute of Technology in Zürich, where he stayed until 1867. During that year, he moved to Würzburg and two years in 1869 to Bonn. In 1870 Clausius organized an ambulance corps in the Franco-Prussian War, he was wounded in battle. He was awarded the Iron Cross for his services, his wife, Adelheid Rimpham, died in childbirth in 1875. He had less time for research thereafter. In 1886, he married Sophie Sack, had another child. Two years on 24 August 1888, he died in Bonn, Germany. Clausius's PhD thesis concerning the refraction of light proposed that we see a blue sky during the day, various shades of red at sunrise and sunset due to reflection and refraction of light. Lord Rayleigh would show that it was in fact due to the scattering of light, but regardless, Clausius used a far more mathematical approach than some have used.
His most famous paper, Ueber die bewegende Kraft der Wärme was published in 1850, dealt with the mechanical theory of heat. In this paper, he showed that there was a contradiction between Carnot's principle and the concept of conservation of energy. Clausius restated the two laws of thermodynamics to overcome this contradiction; this paper made him famous among scientists. Clausius' most famous statement of thermodynamics second law was published in German in 1854, in English in 1856. Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time. During 1857, Clausius contributed to the field of kinetic theory after refining August Krönig's simple gas-kinetic model to include translational and vibrational molecular motions. In this same work he introduced the concept of'Mean free path' of a particle. Clausius deduced the Clausius–Clapeyron relation from thermodynamics; this relation, a way of characterizing the phase transition between two states of matter such as solid and liquid, had been developed in 1834 by Émile Clapeyron.
In 1865, Clausius gave the first mathematical version of the concept of entropy, gave it its name. Clausius chose the word because the meaning is "content transformative" or "transformation content", he used the now abandoned unit'Clausius' for entropy. 1 Clausius = 1 calorie/degree Celsius = 4.1868 joules per kelvin The landmark 1865 paper in which he introduced the concept of entropy ends with the following summary of the first and second laws of thermodynamics: The energy of the universe is constant. The entropy of the universe tends to a maximum. Honorary Membership of the Institution of Engineers and Shipbuilders in Scotland in 1859. Iron Cross of 1870 Fellow of the Royal Society of London in 1868 and received its Copley Medal in 1879. Member of the Royal Swedish Academy of Sciences in 1878. Huygens Medal in 1870. Foreign Member of the Accademia Nazionale dei Lincei in Rome in 1880 Member of the German Academy of Sciences Leopoldina in 1880 Poncelet Prize in 1883. Honorary doctorate from the University of Würzburg in 1882.
Foreign Member of the Royal Netherlands Academy of Arts and Sciences in 1886. Pour le Mérite for Arts and Sciences in 1888 The lunar crater Clausius named in his honor. A memorial in his home town of Koszalin in 2009 Clausius, R.. The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst. English translations of nine papers. Hans Peter Jørgen Julius Thomsen, one of the founders of the thermochemistry. Revival of Kinetic Theory by Clausius O'Connor, John J.. Chisholm, Hugh, ed.. "Clausius, Rudolf Julius Emmanuel". Encyclopædia Britannica. Cambridge University Press. Works by Rudolf Clausius at Project Gutenberg Works by or about Rudolf Clausius at Internet Archive