title: Notting Hill (film)

text: Original music was composed by Trevor Jones. A main score was written, and excerpts were used throughout the film. The score was broken down into two songs for the soundtrack (Will and Anna/Notting Hill). Several additional songs written by other artists include Elvis Costello's cover of the Charles Aznavour song "She". Charles Aznavour's original version can be heard during the opening credits while Elvis Costello's version is played at the end of the movie (before the end credits). Other songs are Shania Twain's remixed version of "You've Got a Way", as well as Ronan Keating's specially recorded cover of "When You Say Nothing at All"; the song reached number one in the British charts. Pulp recorded a new song "Born to Cry", which was released on the European version of the soundtrack album.


title: Notting Hill (film)

text: The song played when Will strides down Portobello Road is "Ain't No Sunshine" by Bill Withers. Tony and Bernie play "Blue Moon" on the piano at Tony's restaurant on the night it closes. Originally, Charles Aznavour's version of "She" was used in the film, but American test screening audiences did not respond to it. Costello was then brought in by Richard Curtis to record a cover version of the song. Both versions of the song appear in non-US releases.


title: Notting Hill (film)

text: The film score and original music was recorded and mixed by Gareth Cousins (who also mixed all the songs used in the film) and Simon Rhodes.


title: Notting Hill (film)

text: The film had its premiere at the Odeon Leicester Square on 27 April 1999 and opened in the UK on 21 May 1999 and in the United States the following week.


title: Notting Hill (film)

text: On Rotten Tomatoes the film holds an approval rating of 84% based on 105 reviews, with an average rating of 7.1/10. The website's critical consensus reads: "A rom-com with the right ingredients, "Notting Hill" proves there's nothing like a love story well told – especially when Hugh Grant and Julia Roberts are your leads." On Metacritic the film has a weighted average score of 68 out of 100 based on 34 critics, indicating "generally favourable reviews". Audiences polled by CinemaScore gave the film an average grade of "B+" on an A+ to F scale.


title: Notting Hill (film)

text: "Variety"'s Derek Elley said that "It's slick, it's gawky, it's 10 minutes too long, and it's certainly not ""Four Weddings and a Funeral" Part 2" in either construction or overall tone", giving it an overall positive review. "Cranky Critic" called it "Bloody damned good", as well as saying that it was "A perfect date flick." "Nitrate" said that ""Notting Hill" is whimsical and light, fresh and quirky", with "endearing moments and memorable characters". In his review of the film's DVD John J. Puccio noted that "the movie is a fairy tale, and writer Richard Curtis knows how much the public loves a fairy tale", calling it "a sweet film". Desson Howe of "The Washington Post" gave the film a very positive review, particularly praising Rhys Ifans' performance as Spike. James Sanford gave "Notting Hill" three and a half stars, saying that "Curtis' dialogue may be much snappier than his sometimes dawdling plot, but the first hour of "Notting Hill" is so beguiling and consistently funny it seems churlish to complain that the rest is merely good." Sue Pierman of the "Milwaukee Journal Sentinel" stated that ""Notting Hill" is clever, funny, romantic– and oh, yes, reminiscent of "Four Weddings and a Funeral"", but that the film "is so satisfying, it doesn't pay to nitpick." Roger Ebert praised the film, saying "the movie is bright, the dialogue has wit and intelligence, and Roberts and Grant are very easy to like." Kenneth Turan gave a good review, concluding that "the film's romantic core is impervious to problems". CNN reviewer Paul Clinton said that "Notting Hill" "stands alone as another funny and heartwarming story about love against all odds".


title: Notting Hill (film)

text: Widgett Walls of Needcoffee.com gave the film "three and a half cups of coffee", stating that "the humor of the film saves it from a completely trite and unsatisfying (nay, shall I say enraging) ending", but criticised the soundtrack. Dennis Schwartz gave the film a negative review with a grade of "C−" citing "this film was pure and unadulterated balderdash". Some criticised the film for giving a "sweetened unrealistic view of London life and British eccentricity." "The Independent" derided the film for being unrealistic. In particular, the film was criticised for failing to reflect the demographic of the area:


title: Notting Hill (film)

text: "only Curtis could write a movie about Notting Hill, London's most diverse borough, and not feature a single black face in it."


title: Notting Hill (film)

text: "Notting Hill" was 95th on the British Film Institute's "list of the all-time top 100 films", based on estimates of each film's British cinema admissions.


title: Notting Hill (film)

text: The film opened over the Memorial Day weekend in the United States and Canada, the same weekend as "", and opened at number two for the weekend, grossing US$27.7million over the 4-day weekend, the biggest opening for a romantic comedy film, beating "My Best Friend's Wedding" (which also starred Julia Roberts). "Notting Hill" made another US$15million the following week. One month after its release, "Notting Hill" lost its record for highest-grossing opening weekend for a romantic comedy film to "Runaway Bride" (again starring Roberts). The film grossed £31 million in the United Kingdom (the second highest-grossing film of 1999 behind "The Phantom Menace") and US$116,089,678 in the United States and Canada (the sixteenth highest-grossing film of 1999), with a worldwide gross of US$363,889,678, making it the highest-grossing British film of all time, surpassing the record set by "Four Weddings and a Funeral" in 1994 (also starring Hugh Grant), and the seventh highest-grossing film of 1999.


title: Notting Hill (film)

text: "Notting Hill" won the Audience Award for Most Popular Film at the BAFTAs in 2000, and was nominated in the categories of The Alexander Korda Award for Outstanding British Film of the Year, and Best Performance by an Actor in a Supporting Role for Rhys Ifans. The film won Best Comedy Film at the British Comedy Awards. The film's soundtrack won Best Soundtrack at the 2000 Brit Awards, beating "Star Wars: Episode I – The Phantom Menace". The film won Best British Film, Best British Director for Roger Michell, and Best British Actor for Hugh Grant at the Empire Awards.


title: Notting Hill (film)

text: The film received three nominations at the Golden Globes, in the categories Best Motion Picture– Comedy/Musical, Best Motion Picture Actor– Comedy/Musical for Hugh Grant, and Best Motion Picture Actress– Comedy/Musical for Julia Roberts.


title: Second law of thermodynamics

text: The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."


title: Second law of thermodynamics

text: The second law of thermodynamics in other versions establishes the concept of entropy as a physical property of a thermodynamic system. It can be used to predict whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.


title: Second law of thermodynamics

text: Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics provides a microscopic explanation of the law in terms of probability distributions of the states of large assemblies of atoms or molecules. The second law has been expressed in many ways. Its first formulation, which preceded the proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that the efficiency of conversion of heat to work in a heat engine has an upper limit. The first rigorous definition of the second law based on the concept of entropy came from German scientist Rudolf Clausius in the 1850s and included his statement that heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.


title: Second law of thermodynamics

text: The second law of thermodynamics allows the definition of the concept of thermodynamic temperature, relying also on the zeroth law of thermodynamics.


title: Second law of thermodynamics

text: The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system, and expresses its change for a closed system in terms of work and heat. It can be linked to the law of conservation of energy. The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense, and is not reversible. For example, when a path for conduction or radiation is made available, heat always flows spontaneously from a hotter to a colder body. Such phenomena are accounted for in terms of entropy change. If an isolated system containing distinct subsystems is held initially in internal thermodynamic equilibrium by internal partitioning by impermeable walls between the subsystems, and then some operation makes the walls more permeable, then the system spontaneously evolves to reach a final new internal thermodynamic equilibrium, and its total entropy, formula_1, increases.


title: Second law of thermodynamics

text: In a reversible or quasi-static, idealized process of transfer of energy as heat to a closed thermodynamic system of interest, (which allows the entry or exit of energy – but not transfer of matter), from an auxiliary thermodynamic system, an infinitesimal increment (formula_2) in the entropy of the system of interest is defined to result from an infinitesimal transfer of heat (formula_3) to the system of interest, divided by the common thermodynamic temperature formula_4 of the system of interest and the auxiliary thermodynamic system:


title: Second law of thermodynamics

text: Different notations are used for an infinitesimal amount of heat formula_6 and infinitesimal change of entropy formula_7 because entropy is a function of state, while heat, like work, is not.


title: Second law of thermodynamics

text: For an actually possible infinitesimal process without exchange of mass with the surroundings, the second law requires that the increment in system entropy fulfills the inequality


title: Second law of thermodynamics

text: This is because a general process for this case (no mass exchange between the system and its surroundings) may include work being done on the system by its surroundings, which can have frictional or viscous effects inside the system, because a chemical reaction may be in progress, or because heat transfer actually occurs only irreversibly, driven by a finite difference between the system temperature () and the temperature of the surroundings ().


title: Second law of thermodynamics

text: Note that the equality still applies for pure heat flow (only heat flow, no change in chemical composition and mass),


title: Second law of thermodynamics

text: which is the basis of the accurate determination of the absolute entropy of pure substances from measured heat capacity curves and entropy changes at phase transitions, i.e. by calorimetry.


title: Second law of thermodynamics

text: Introducing a set of internal variables formula_10 to describe the deviation of a thermodynamic system from a chemical equilibrium state in physical equilibrium (with the required well-defined uniform pressure "P" and temperature "T"), one can record the equality


title: Second law of thermodynamics

text: The second term represents work of internal variables that can be perturbed by external influences, but the system cannot perform any positive work via internal variables. This statement introduces the impossibility of the reversion of evolution of the thermodynamic system in time and can be considered as a formulation of "the second principle of thermodynamics" – the formulation, which is, of course, equivalent to the formulation of the principle in terms of entropy.


title: Second law of thermodynamics

text: The zeroth law of thermodynamics in its usual short statement allows recognition that two bodies in a relation of thermal equilibrium have the same temperature, especially that a test body has the same temperature as a reference thermometric body. For a body in thermal equilibrium with another, there are indefinitely many empirical temperature scales, in general respectively depending on the properties of a particular reference thermometric body. The second law allows a distinguished temperature scale, which defines an absolute, thermodynamic temperature, independent of the properties of any particular reference thermometric body.


title: Second law of thermodynamics

text: The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.


title: Second law of thermodynamics

text: The historical origin of the second law of thermodynamics was in Sadi Carnot's theoretical analysis of the flow of heat in steam engines (1824). The centerpiece of that analysis, now known as a Carnot engine, is an ideal heat engine fictively operated in the limiting mode of extreme slowness known as quasi-static, so that the heat and work transfers are between subsystems that are always in their own internal states of thermodynamic equilibrium. It represents the theoretical maximum efficiency of a heat engine operating between any two given thermal or heat reservoirs at different temperatures. Carnot's principle was recognized by Carnot at a time when the caloric theory represented the dominant understanding of the nature of heat, before the recognition of the first law of thermodynamics, and before the mathematical expression of the concept of entropy. Interpreted in the light of the first law, Carnot's analysis is physically equivalent to the second law of thermodynamics, and remains valid today. Some samples from his book are:


title: Second law of thermodynamics

text: The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the "Clausius statement":


title: Second law of thermodynamics

text: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.


title: Second law of thermodynamics

text: The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.


title: Second law of thermodynamics

text: Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat is transferred from cold to hot, but only when forced by an external agent, the refrigeration system.


title: Second law of thermodynamics

text: Suppose there is an engine violating the Kelvin statement: i.e., one that drains heat and converts it completely into work (The drained heat is fully converted to work.) in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the right figure. The efficiency of a normal heat engine is "η" and so the efficiency of the reversed heat engine is 1/"η". The net and sole effect of the combined pair of engines is to transfer heat formula_12 from the cooler reservoir to the hotter one, which violates the Clausius statement. This is a consequence of the first law of thermodynamics, as for the total system's energy to remain the same; formula_13, so therefore formula_14, where (1) the sign convention of heat is used in which heat entering into (leaving from) an engine is positive (negative) and (2) formula_15 is obtained by the definition of efficiency of the engine when the engine operation is not reversed. Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.


title: Second law of thermodynamics

text: Planck offered the following proposition as derived directly from experience. This is sometimes regarded as his statement of the second law, but he regarded it as a starting point for the derivation of the second law.


title: Second law of thermodynamics

text: It is almost customary in textbooks to speak of the "Kelvin–Planck statement" of the law, as for example in the text by ter Haar and Wergeland. This version, also known as the heat engine statement, of the second law states that


title: Second law of thermodynamics

text: Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:


title: Second law of thermodynamics

text: In every neighborhood of any state S of an adiabatically enclosed system there are states inaccessible from S.


title: Second law of thermodynamics

text: With this formulation, he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, formula_16.


title: Second law of thermodynamics

text: Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.


title: Second law of thermodynamics

text: In 1926, Max Planck wrote an important paper on the basics of thermodynamics. He indicated the principle


title: Second law of thermodynamics

text: This formulation does not mention heat and does not mention temperature, nor even entropy, and does not necessarily implicitly rely on those concepts, but it implies the content of the second law. A closely related statement is that "Frictional pressure never does positive work." Planck wrote: "The production of heat by friction is irreversible."


title: Second law of thermodynamics

text: Not mentioning entropy, this principle of Planck is stated in physical terms. It is very closely related to the Kelvin statement given just above. It is relevant that for a system at constant volume and mole numbers, the entropy is a monotonic function of the internal energy. Nevertheless, this principle of Planck is not actually Planck's preferred statement of the second law, which is quoted above, in a previous sub-section of the present section of this present article, and relies on the concept of entropy.


title: Second law of thermodynamics

text: A statement that in a sense is complementary to Planck's principle is made by Borgnakke and Sonntag. They do not offer it as a full statement of the second law:


title: Second law of thermodynamics

text: Differing from Planck's just foregoing principle, this one is explicitly in terms of entropy change. Removal of matter from a system can also decrease its entropy.


title: Second law of thermodynamics

text: The second law has been shown to be equivalent to the internal energy "U" being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).


title: Second law of thermodynamics

text: Before the establishment of the second law, many people who were interested in inventing a perpetual motion machine had tried to circumvent the restrictions of first law of thermodynamics by extracting the massive internal energy of the environment as the power of the machine. Such a machine is called a "perpetual motion machine of the second kind". The second law declared the impossibility of such machines.


title: Second law of thermodynamics

text: Carnot's theorem (1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states:


title: Second law of thermodynamics

text: In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realize the Carnot cycle's reversibility and was condemned to be less efficient.


title: Second law of thermodynamics

text: Though formulated in terms of caloric (see the obsolete caloric theory), rather than entropy, this was an early insight into the second law.


title: Second law of thermodynamics

text: The equality holds in the reversible case and the strict inequality holds in the irreversible case, with "T" as the temperature of the heat bath (surroundings) here. The reversible case is used to introduce the state function entropy. This is because in cyclic processes the variation of a state function is zero from state functionality.


title: Second law of thermodynamics

text: where "W" is the net work done by the engine per cycle, "q" > 0 is the heat added to the engine from a hot reservoir, and "q" = - |"q"| < 0 is waste heat given off to a cold reservoir from the engine. Thus the efficiency depends only on the ratio |"q"| / |"q"|.


title: Second law of thermodynamics

text: Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, any reversible heat engine operating between temperatures "T" and "T" must have the same efficiency, that is to say, the efficiency is a function of temperatures only:


title: Second law of thermodynamics

text: In addition, a reversible heat engine operating between temperatures "T" and "T" must have the same efficiency as one consisting of two cycles, one between "T" and another (intermediate) temperature "T", and the second between "T" and "T", where "T" > "T" > "T". This is because, if a part of the two cycle engine is hidden such that it is recognized as an engine between the reservoirs at the temperatures "T" and "T", then the efficiency of this engine must be same to the other engine at the same reservoirs. If we choose engines such that work done by the one cycle engine and the two cycle engine are same, then the efficiency of each heat engine is written as the below.


title: Second law of thermodynamics

text: Here, the engine 1 is the one cycle engine, and the engines 2 and 3 make the two cycle engine where there is the intermediate reservoir at "T". We also have used the fact that the heat formula_21 passes through the intermediate thermal reservoir at formula_22 without losing its energy. (I.e., formula_21 is not lost during its passage through the reservoir at formula_22.) This fact can be proved by the following.


title: Second law of thermodynamics

text: In order to have the consistency in the last equation, the heat formula_21 flown from the engine 2 to the intermediate reservoir must be equal to the heat formula_27 flown out from the reservoir to the engine 3.


title: Second law of thermodynamics

text: Now consider the case where formula_29 is a fixed reference temperature: the temperature of the triple point of water as 273.16 Kelvin; formula_30. Then for any "T" and "T",


title: Second law of thermodynamics

text: and the reference temperature "T"* = 273.16 K × "f"("T","T") = 273.16 K. (Any reference temperature and any positive numerical value could be usedthe choice here corresponds to the Kelvin scale.)


title: Second law of thermodynamics

text: So we can define a state function S called entropy, which for a reversible process or for pure heat transfer satisfies


title: Second law of thermodynamics

text: With this we can only obtain the difference of entropy by integrating the above formula. To obtain the absolute value, we need the third law of thermodynamics, which states that "S" = 0 at absolute zero for perfect crystals.


title: Second law of thermodynamics

text: For any irreversible process, since entropy is a state function, we can always connect the initial and terminal states with an imaginary reversible process and integrating on that path to calculate the difference in entropy.


title: Second law of thermodynamics

text: Now reverse the reversible process and combine it with the said irreversible process. Applying the Clausius inequality on this loop, with "T" as the temperature of the surroundings,


title: Second law of thermodynamics

text: An important and revealing idealized special case is to consider applying the second law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an "unlimited" heat reservoir at temperature "T" and pressure "P" so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain "T"; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain "P".


title: Second law of thermodynamics

text: Whatever changes to "dS" and "dS" occur in the entropies of the sub-system and the surroundings individually, the entropy "S" of the isolated total system must not decrease according to the second law of thermodynamics:


title: Second law of thermodynamics

text: According to the first law of thermodynamics, the change "dU" in the internal energy of the sub-system is the sum of the heat "δq" added to the sub-system, "less" any work "δw" done "by" the sub-system, "plus" any net chemical energy entering the sub-system "d" Σ"μN", so that:


title: Second law of thermodynamics

text: where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the Second Law inequality from above.


title: Second law of thermodynamics

text: It is useful to separate the work "δw" done by the subsystem into the "useful" work "δw" that can be done "by" the sub-system, over and beyond the work "p dV" done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:


title: Second law of thermodynamics

text: It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the "availability" or "exergy" "E" of the subsystem,


title: Second law of thermodynamics

text: The Second Law therefore implies that for any process which can be considered as divided simply into a subsystem, and an unlimited temperature and pressure reservoir with which it is in contact,


title: Second law of thermodynamics

text: i.e. the change in the subsystem's exergy plus the useful work done "by" the subsystem (or, the change in the subsystem's exergy less any work, additional to that done by the pressure reservoir, done "on" the system) must be less than or equal to zero.


title: Second law of thermodynamics

text: In sum, if a proper "infinite-reservoir-like" reference state is chosen as the system surroundings in the real world, then the second law predicts a decrease in "E" for an irreversible process and no change for a reversible process.


title: Second law of thermodynamics

text: This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the second law without directly measuring or considering entropy change in a total isolated system. ("Also, see process engineer"). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found ("See second law efficiency".)


title: Second law of thermodynamics

text: This approach to the second law is widely utilized in engineering practice, environmental accounting, systems ecology, and other disciplines.


title: Second law of thermodynamics

text: The second law determines whether a proposed physical or chemical process is forbidden or may occur spontaneously. For isolated systems, no energy is provided by the surroundings and the second law requires that the entropy of the system alone must increase: Δ"S" > 0. Examples of spontaneous physical processes in isolated systems include the following:


title: Second law of thermodynamics

text: However, for some non-isolated systems which can exchange energy with their surroundings, the surroundings exchange enough heat with the system, or do sufficient work on the system, so that the processes occur in the opposite direction. This is possible provided the total entropy change of the system plus the surroundings is positive as required by the second law: Δ"S" = Δ"S" + Δ"S" > 0. For the three examples given above:


title: Second law of thermodynamics

text: For a spontaneous chemical process in a closed system at constant temperature and pressure without non-"PV" work, the Clausius inequality Δ"S" > "Q/T" transforms into a condition for the change in Gibbs free energy


title: Second law of thermodynamics

text: or d"G" < 0. For a similar process at constant temperature and volume, the change in Helmholtz free energy must be negative, formula_51. Thus, a negative value of the change in free energy ("G" or "A") is a necessary condition for a process to be spontaneous. This is the most useful form of the second law of thermodynamics in chemistry, where free-energy changes can be calculated from tabulated enthalpies of formation and standard molar entropies of reactants and products. The chemical equilibrium condition at constant "T" and "p" without electrical work is d"G" = 0.


title: Second law of thermodynamics

text: The first theory of the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its surroundings.


title: Second law of thermodynamics

text: Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law during 1850, in this form: heat does not flow "spontaneously" from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).


title: Second law of thermodynamics

text: Established during the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.


title: Second law of thermodynamics

text: The ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.


title: Second law of thermodynamics

text: There is a traditional doctrine, starting with Clausius, that entropy can be understood in terms of molecular 'disorder' within a macroscopic system. This doctrine is obsolescent.


title: Second law of thermodynamics

text: In 1865, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:


title: Second law of thermodynamics

text: where "Q" is heat, "T" is temperature and "N" is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:


title: Second law of thermodynamics

text: This statement is the best-known phrasing of the second law. Because of the looseness of its language, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This is not true; this statement is only a simplified version of a more extended and precise description.


title: Second law of thermodynamics

text: In terms of time variation, the mathematical statement of the second law for an isolated system undergoing an arbitrary transformation is:


title: Second law of thermodynamics

text: The equality sign applies after equilibration. An alternative way of formulating of the second law for isolated systems is:


title: Second law of thermodynamics

text: with formula_56 the sum of the rate of entropy production by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature formula_57 it gives the so-called dissipated energy formula_58.


title: Second law of thermodynamics

text: The expression of the second law for closed systems (so, allowing heat exchange and moving boundaries, but not exchange of matter) is:


title: Second law of thermodynamics

text: The equality sign holds in the case that only reversible processes take place inside the system. If irreversible processes take place (which is the case in real systems in operation) the >-sign holds. If heat is supplied to the system at several places we have to take the algebraic sum of the corresponding terms.


title: Second law of thermodynamics

text: Here formula_65 is the flow of entropy into the system associated with the flow of matter entering the system. It should not be confused with the time derivative of the entropy. If matter is supplied at several places we have to take the algebraic sum of these contributions.


title: Second law of thermodynamics

text: Statistical mechanics gives an explanation for the second law by postulating that a material is composed of atoms and molecules which are in constant motion. A particular set of positions and velocities for each particle in the system is called a microstate of the system and because of the constant motion, the system is constantly changing its microstate. Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur, and when this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/ where "N" is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law. Classical thermodynamic theory does not deal with these statistical variations.


title: Second law of thermodynamics

text: The first mechanical argument of the Kinetic theory of gases that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium was due to James Clerk Maxwell in 1860; Ludwig Boltzmann with his H-theorem of 1872 also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution.


title: Second law of thermodynamics

text: Due to Loschmidt's paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested.


title: Second law of thermodynamics

text: Given these assumptions, in statistical mechanics, the Second Law is not a postulate, rather it is a consequence of the fundamental postulate, also known as the equal prior probability postulate, so long as one is clear that simple probability arguments are applied only to the future, while for the past there are auxiliary sources of information which tell us that it was low entropy. The first part of the second law, which states that the entropy of a thermally isolated system can only increase, is a trivial consequence of the equal prior probability postulate, if we restrict the notion of the entropy to systems in thermal equilibrium. The entropy of an isolated system in thermal equilibrium containing an amount of energy of formula_66 is:


title: Second law of thermodynamics

text: where formula_68 is the number of quantum states in a small interval between formula_66 and formula_70. Here formula_71 is a macroscopically small energy interval that is kept fixed. Strictly speaking this means that the entropy depends on the choice of formula_71. However, in the thermodynamic limit (i.e. in the limit of infinitely large system size), the specific entropy (entropy per unit volume or per unit mass) does not depend on formula_71.


title: Second law of thermodynamics

text: Suppose we have an isolated system whose macroscopic state is specified by a number of variables. These macroscopic variables can, e.g., refer to the total volume, the positions of pistons in the system, etc. Then formula_74 will depend on the values of these variables. If a variable is not fixed, (e.g. we do not clamp a piston in a certain position), then because all the accessible states are equally likely in equilibrium, the free variable in equilibrium will be such that formula_74 is maximized at the given energy of the isolated system as that is the most probable situation in equilibrium.


title: Second law of thermodynamics

text: If the variable was initially fixed to some value then upon release and when the new equilibrium has been reached, the fact the variable will adjust itself so that formula_74 is maximized, implies that the entropy will have increased or it will have stayed the same (if the value at which the variable was fixed happened to be the equilibrium value).


title: Second law of thermodynamics

text: Suppose we start from an equilibrium situation and we suddenly remove a constraint on a variable. Then right after we do this, there are a number formula_74 of accessible microstates, but equilibrium has not yet been reached, so the actual probabilities of the system being in some accessible state are not yet equal to the prior probability of formula_78. We have already seen that in the final equilibrium state, the entropy will have increased or have stayed the same relative to the previous equilibrium state. Boltzmann's H-theorem, however, proves that the quantity increases monotonically as a function of time during the intermediate out of equilibrium state.


title: Second law of thermodynamics

text: The second part of the Second Law states that the entropy change of a system undergoing a reversible process is given by:


title: Second law of thermodynamics

text: See here for the justification for this definition. Suppose that the system has some external parameter, "x", that can be changed. In general, the energy eigenstates of the system will depend on "x". According to the adiabatic theorem of quantum mechanics, in the limit of an infinitely slow change of the system's Hamiltonian, the system will stay in the same energy eigenstate and thus change its energy according to the change in energy of the energy eigenstate it is in.


title: Second law of thermodynamics

text: The generalized force, "X", corresponding to the external variable "x" is defined such that formula_81 is the work performed by the system if "x" is increased by an amount "dx". For example, if "x" is the volume, then "X" is the pressure. The generalized force for a system known to be in energy eigenstate formula_82 is given by:


title: Second law of thermodynamics

text: Since the system can be in any energy eigenstate within an interval of formula_71, we define the generalized force for the system as the expectation value of the above expression:


title: Second law of thermodynamics

text: To evaluate the average, we partition the formula_68 energy eigenstates by counting how many of them have a value for formula_87 within a range between formula_88 and formula_89. Calling this number formula_90, we have:


title: Second law of thermodynamics

text: We can relate this to the derivative of the entropy with respect to "x" at constant energy "E" as follows. Suppose we change "x" to "x" + "dx". Then formula_68 will change because the energy eigenstates depend on "x", causing energy eigenstates to move into or out of the range between formula_66 and formula_95. Let's focus again on the energy eigenstates for which formula_96 lies within the range between formula_88 and formula_89. Since these energy eigenstates increase in energy by "Y dx", all such energy eigenstates that are in the interval ranging from "E" – "Y" "dx" to "E" move from below "E" to above "E". There are


title: Second law of thermodynamics

text: such energy eigenstates. If formula_100, all these energy eigenstates will move into the range between formula_66 and formula_95 and contribute to an increase in formula_74. The number of energy eigenstates that move from below formula_95 to above formula_95 is given by formula_106. The difference


title: Second law of thermodynamics

text: is thus the net contribution to the increase in formula_74. Note that if "Y dx" is larger than formula_71 there will be the energy eigenstates that move from below "E" to above formula_95. They are counted in both formula_111 and formula_106, therefore the above expression is also valid in that case.


title: Second law of thermodynamics

text: Expressing the above expression as a derivative with respect to "E" and summing over "Y" yields the expression:


title: Second law of thermodynamics

text: The first term is intensive, i.e. it does not scale with system size. In contrast, the last term scales as the inverse system size and will thus vanish in the thermodynamic limit. We have thus found that:


title: Second law of thermodynamics

text: If a system is in thermal contact with a heat bath at some temperature "T" then, in equilibrium, the probability distribution over the energy eigenvalues are given by the canonical ensemble:


title: Second law of thermodynamics

text: Here "Z" is a factor that normalizes the sum of all the probabilities to 1, this function is known as the partition function. We now consider an infinitesimal reversible change in the temperature and in the external parameters on which the energy levels depend. It follows from the general formula for the entropy:


title: Second law of thermodynamics

text: As elaborated above, it is thought that the second law of thermodynamics is a result of the very low-entropy initial conditions at the Big Bang. From a statistical point of view, these were very special conditions. On the other hand, they were quite simple, as the universe - or at least the part thereof from which the observable universe developed - seems to have been extremely uniform.


title: Second law of thermodynamics

text: This may seem somewhat paradoxical, since in many physical systems uniform conditions (e.g. mixed rather than separated gases) have high entropy. The paradox is solved once realizing that gravitational systems have negative heat capacity, so that when gravity is important, uniform conditions (e.g. gas of uniform density) in fact have lower entropy compared to non-uniform ones (e.g. black holes in empty space). Yet another approach is that the universe had high (or even maximal) entropy given its size, but as the universe grew it rapidly came out of thermodynamic equilibrium, its entropy only slightly increased compared to the increase in maximal possible entropy, and thus it has arrived at a very low entropy when compared to the much larger possible maximum given its later size.


title: Second law of thermodynamics

text: As for the reason why initial conditions were such, one suggestion is that cosmological inflation was enough to wipe off non-smoothness, while another is that the universe was created spontaneously where the mechanism of creation implies low-entropy initial conditions.


title: Second law of thermodynamics

text: There are two principal ways of formulating thermodynamics, (a) through passages from one state of thermodynamic equilibrium to another, and (b) through cyclic processes, by which the system is left unchanged, while the total entropy of the surroundings is increased. These two ways help to understand the processes of life. The thermodynamics of living organisms has been considered by many authors, such as Erwin Schrödinger, Léon Brillouin and Isaac Asimov.


title: Second law of thermodynamics

text: To a fair approximation, living organisms may be considered as examples of (b). Approximately, an animal's physical state cycles by the day, leaving the animal nearly unchanged. Animals take in food, water, and oxygen, and, as a result of metabolism, give out breakdown products and heat. Plants take in radiative energy from the sun, which may be regarded as heat, and carbon dioxide and water. They give out oxygen. In this way they grow. Eventually they die, and their remains rot away, turning mostly back into carbon dioxide and water. This can be regarded as a cyclic process. Overall, the sunlight is from a high temperature source, the sun, and its energy is passed to a lower temperature sink, i.e. radiated into space. This is an increase of entropy of the surroundings of the plant. Thus animals and plants obey the second law of thermodynamics, considered in terms of cyclic processes.


title: Second law of thermodynamics

text: Furthermore, the ability of living organisms to grow and increase in complexity, as well as to form correlations with their environment in the form of adaption and memory, is not opposed to the second law – rather, it is akin to general results following from it: Under some definitions, an increase in entropy also results in an increase in complexity, and for a finite system interacting with finite reservoirs, an increase in entropy is equivalent to an increase in correlations between the system and the reservoirs.


title: Second law of thermodynamics

text: Living organisms may be considered as open systems, because matter passes into and out from them. Thermodynamics of open systems is currently often considered in terms of passages from one state of thermodynamic equilibrium to another, or in terms of flows in the approximation of local thermodynamic equilibrium. The problem for living organisms may be further simplified by the approximation of assuming a steady state with unchanging flows. General principles of entropy production for such approximations are subject to an unsettled current debate or research.


title: Second law of thermodynamics

text: Commonly, systems for which gravity is not important have a positive heat capacity, meaning that their temperature rises with their internal energy. Therefore, when energy flows from a high-temperature object to a low-temperature object, the source temperature decreases while the sink temperature is increased; hence temperature differences tend to diminish over time.


title: Second law of thermodynamics

text: This is not always the case for systems in which the gravitational force is important: systems that are bound by their own gravity, such as stars, can have negative heat capacities. As they contract, both their total energy and their entropy decrease but their internal temperature may increase. This can be significant for protostars and even gas giant planets such as Jupiter.


title: Second law of thermodynamics

text: As gravity is the most important force operating on cosmological scales, it may be difficult or impossible to apply the second law to the universe as a whole.


title: Second law of thermodynamics

text: The theory of classical or equilibrium thermodynamics is idealized. A main postulate or assumption, often not even explicitly stated, is the existence of systems in their own internal states of thermodynamic equilibrium. In general, a region of space containing a physical system at a given time, that may be found in nature, is not in thermodynamic equilibrium, read in the most stringent terms. In looser terms, nothing in the entire universe is or has ever been truly in exact thermodynamic equilibrium.


title: Second law of thermodynamics

text: For purposes of physical analysis, it is often enough convenient to make an assumption of thermodynamic equilibrium. Such an assumption may rely on trial and error for its justification. If the assumption is justified, it can often be very valuable and useful because it makes available the theory of thermodynamics. Elements of the equilibrium assumption are that a system is observed to be unchanging over an indefinitely long time, and that there are so many particles in a system, that its particulate nature can be entirely ignored. Under such an equilibrium assumption, in general, there are no macroscopically detectable fluctuations. There is an exception, the case of critical states, which exhibit to the naked eye the phenomenon of critical opalescence. For laboratory studies of critical states, exceptionally long observation times are needed.


title: Second law of thermodynamics

text: In all cases, the assumption of thermodynamic equilibrium, once made, implies as a consequence that no putative candidate "fluctuation" alters the entropy of the system.


title: Second law of thermodynamics

text: It can easily happen that a physical system exhibits internal macroscopic changes that are fast enough to invalidate the assumption of the constancy of the entropy. Or that a physical system has so few particles that the particulate nature is manifest in observable fluctuations. Then the assumption of thermodynamic equilibrium is to be abandoned. There is no unqualified general definition of entropy for non-equilibrium states.


title: Second law of thermodynamics

text: There are intermediate cases, in which the assumption of local thermodynamic equilibrium is a very good approximation, but strictly speaking it is still an approximation, not theoretically ideal.


title: Second law of thermodynamics

text: For non-equilibrium situations in general, it may be useful to consider statistical mechanical definitions of other quantities that may be conveniently called 'entropy', but they should not be confused or conflated with thermodynamic entropy properly defined for the second law. These other quantities indeed belong to statistical mechanics, not to thermodynamics, the primary realm of the second law.


title: Second law of thermodynamics

text: The second law of thermodynamics is a physical law that is not symmetric to reversal of the time direction. This does not conflict with symmetries observed in the fundamental laws of physics (particularly CPT symmetry) since the second law applies statistically on time-asymmetric boundary conditions. The second law has been related to the difference between moving forwards and backwards in time, or to the principle that cause precedes effect (the causal arrow of time, or causality).


title: Second law of thermodynamics

text: Irreversibility in thermodynamic processes is a consequence of the asymmetric character of thermodynamic operations, and not of any internally irreversible microscopic properties of the bodies. Thermodynamic operations are macroscopic external interventions imposed on the participating bodies, not derived from their internal properties. There are reputed "paradoxes" that arise from failure to recognize this.


title: Second law of thermodynamics

text: Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from the time-symmetric dynamics that describe the microscopic evolution of a macroscopic system.


title: Second law of thermodynamics

text: In the opinion of Schrödinger, "It is now quite obvious in what manner you have to reformulate the law of entropyor for that matter, all other irreversible statementsso that they be capable of being derived from reversible models. You must not speak of one isolated system but at least of two, which you may for the moment consider isolated from the rest of the world, but not always from each other." The two systems are isolated from each other by the wall, until it is removed by the thermodynamic operation, as envisaged by the law. The thermodynamic operation is externally imposed, not subject to the reversible microscopic dynamical laws that govern the constituents of the systems. It is the cause of the irreversibility. The statement of the law in this present article complies with Schrödinger's advice. The cause–effect relation is logically prior to the second law, not derived from it.


title: Second law of thermodynamics

text: The Poincaré recurrence theorem considers a theoretical microscopic description of an isolated physical system. This may be considered as a model of a thermodynamic system after a thermodynamic operation has removed an internal wall. The system will, after a sufficiently long time, return to a microscopically defined state very close to the initial one. The Poincaré recurrence time is the length of time elapsed until the return. It is exceedingly long, likely longer than the life of the universe, and depends sensitively on the geometry of the wall that was removed by the thermodynamic operation. The recurrence theorem may be perceived as apparently contradicting the second law of thermodynamics. More obviously, however, it is simply a microscopic model of thermodynamic equilibrium in an isolated system formed by removal of a wall between two systems. For a typical thermodynamical system, the recurrence time is so large (many many times longer than the lifetime of the universe) that, for all practical purposes, one cannot observe the recurrence. One might wish, nevertheless, to imagine that one could wait for the Poincaré recurrence, and then re-insert the wall that was removed by the thermodynamic operation. It is then evident that the appearance of irreversibility is due to the utter unpredictability of the Poincaré recurrence given only that the initial state was one of thermodynamic equilibrium, as is the case in macroscopic thermodynamics. Even if one could wait for it, one has no practical possibility of picking the right instant at which to re-insert the wall. The Poincaré recurrence theorem provides a solution to Loschmidt's paradox. If an isolated thermodynamic system could be monitored over increasingly many multiples of the average Poincaré recurrence time, the thermodynamic behavior of the system would become invariant under time reversal.


title: Second law of thermodynamics

text: James Clerk Maxwell imagined one container divided into two parts, "A" and "B". Both parts are filled with the same gas at equal temperatures and placed next to each other, separated by a wall. Observing the molecules on both sides, an imaginary demon guards a microscopic trapdoor in the wall. When a faster-than-average molecule from "A" flies towards the trapdoor, the demon opens it, and the molecule will fly from "A" to "B". The average speed of the molecules in "B" will have increased while in "A" they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in "A" and increases in "B", contrary to the second law of thermodynamics.


title: Second law of thermodynamics

text: One response to this question was suggested in 1929 by Leó Szilárd and later by Léon Brillouin. Szilárd pointed out that a real-life Maxwell's demon would need to have some means of measuring molecular speed, and that the act of acquiring information would require an expenditure of energy.


title: Second law of thermodynamics

text: Maxwell's 'demon' repeatedly alters the permeability of the wall between "A" and "B". It is therefore performing thermodynamic operations on a microscopic scale, not just observing ordinary spontaneous or natural macroscopic thermodynamic processes.


title: Torque

text: In physics and mechanics, torque is a standard mechanical quantity, the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of the body. The concept originated with the studies by Archimedes of the usage of levers, which is reflected in his famous quote: ""Give me a lever and a place to stand and I will move the Earth"". Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. The law of conservation of energy can also be used to understand torque. The symbol for torque is typically formula_1, the lowercase Greek letter "tau". When being referred to as moment of force, it is commonly denoted by .


title: Torque

text: In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the "lever arm vector" connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:


title: Torque

text: The term "torque" (from Latin "torquēre" "to twist") is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in the first edition of "Dynamo-Electric Machinery". Thompson motivates the term as follows:


title: Torque

text: Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows the definition used in US physics in its usage of the word "torque".


title: Torque

text: In the UK and in US mechanical engineering, torque is referred to as "moment of force", usually shortened to "moment". That term has been attested in French since at least 1811 by Siméon Denis Poisson in "Traité de mécanique". An English translation of that work appears in 1842.


title: Torque

text: A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum (the length of the lever arm) is its torque. A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. The direction of the torque can be determined by using the right hand grip rule: if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque.


title: Torque

text: More generally, the torque on a point particle (which has the position r in some reference frame) can be defined as the cross product:


title: Torque

text: where "F" is the magnitude of the force applied, and "θ" is the angle between the position and force vectors. Alternatively,


title: Torque

text: where "F" is the amount of force directed perpendicularly to the position of the particle. Any force directed parallel to the particle's position vector does not produce a torque.


title: Torque

text: It follows from the properties of the cross product that the "torque vector" is perpendicular to both the "position" and "force" vectors. Conversely, the "torque vector" defines the plane in which the "position" and "force" vectors lie. The resulting "torque vector" direction is determined by the right-hand rule.


title: Torque

text: where α is the angular acceleration of the particle, and "p" is the radial component of its linear momentum. This equation is the rotational analogue of Newton's Second Law for point particles, and is valid for any type of trajectory. Note that although force and acceleration are always parallel and directly proportional, the torque τ need not be parallel or directly proportional to the angular acceleration α. This arises from the fact that although mass is always conserved, the moment of inertia in general is not.


title: Torque

text: In some simple cases like a rotating disc, the moment of inertia is a constant, the rotational Newton's Second Law can be


title: Torque

text: where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is:


title: Torque

text: This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definition of force formula_21 (whether or not mass is constant) and the definition of velocity formula_22


title: Torque

text: The cross product of momentum formula_24 with its associated velocity formula_25 is zero because velocity and momentum are parallel, so the second term vanishes.


title: Torque

text: The proof can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass.


title: Torque

text: Torque has the dimension of force times distance, symbolically . Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit "newton-metre" (N⋅m) and never the joule. The unit "newton metre" is properly denoted N⋅m.


title: Torque

text: The traditional imperial and U.S. customary units for torque are the pound foot (lbf-ft), or for small values the pound inch (lbf-in). In the US, torque is most commonly referred to as the foot-pound (denoted as either lb-ft or ft-lb) and the inch-pound (denoted as in-lb). Practitioners depend on context and the hyphen in the abbreviation to know that these refer to torque and not to energy or moment of mass (as the symbolism ft-lb would properly imply).


title: Torque

text: A very useful special case, often given as the definition of torque in fields other than physics, is as follows:


title: Torque

text: The construction of the "moment arm" is shown in the figure to the right, along with the vectors r and F mentioned above. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force is perpendicular to the displacement vector r, the moment arm will be equal to the distance to the centre, and torque will be a maximum for the given force. The equation for the magnitude of a torque, arising from a perpendicular force:


title: Torque

text: For example, if a person places a force of 10 N at the terminal end of a wrench that is 0.5 m long (or a force of 10 N acting 0.5 m from the twist point of a wrench of any length), the torque will be 5 N⋅m – assuming that the person moves the wrench by applying force in the plane of movement and perpendicular to the wrench.


title: Torque

text: For an object to be in static equilibrium, not only must the sum of the forces be zero, but also the sum of the torques (moments) about any point. For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: and , and the torque a third equation: . That is, to solve statically determinate equilibrium problems in two-dimensions, three equations are used.


title: Torque

text: When the net force on the system is zero, the torque measured from any point in space is the same. For example, the torque on a current-carrying loop in a uniform magnetic field is the same regardless of the point of reference. If the net force formula_29 is not zero, and formula_30 is the torque measured from formula_31, then the torque measured from formula_32 is


title: Torque

text: Torque forms part of the basic specification of an engine: the power output of an engine is expressed as its torque multiplied by the angular speed of the drive shaft. Internal-combustion engines produce useful torque only over a limited range of rotational speeds (typically from around 1,000–6,000 rpm for a small car). One can measure the varying torque output over that range with a dynamometer, and show it as a torque curve.


title: Torque

text: Steam engines and electric motors tend to produce maximum torque close to zero rpm, with the torque diminishing as rotational speed rises (due to increasing friction and other constraints). Reciprocating steam-engines and electric motors can start heavy loads from zero rpm without a clutch.


title: Torque

text: If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass, the work "W" can be expressed as


title: Torque

text: where "τ" is torque, and "θ" and "θ" represent (respectively) the initial and final angular positions of the body.


title: Torque

text: The work done by a variable force acting over a finite linear displacement formula_35 is given by integrating the force with respect to an elemental linear displacement formula_36


title: Torque

text: However, the infinitesimal linear displacement formula_36 is related to a corresponding angular displacement formula_39 and the radius vector formula_40 as


title: Torque

text: The expression formula_43 is a scalar triple product given by formula_44. An alternate expression for the same scalar triple product is


title: Torque

text: Since the parameter of integration has been changed from linear displacement to angular displacement, the limits of the integration also change correspondingly, giving


title: Torque

text: If the torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., formula_49 giving


title: Torque

text: It follows from the work–energy principle that "W" also represents the change in the rotational kinetic energy "E" of the body, given by


title: Torque

text: where "P" is power, τ is torque, ω is the angular velocity, and formula_53 represents the scalar product.


title: Torque

text: Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any).


title: Torque

text: In practice, this relationship can be observed in bicycles: Bicycles are typically composed of two road wheels, front and rear gears (referred to as sprockets) meshing with a chain, and a derailleur mechanism if the bicycle's transmission system allows multiple gear ratios to be used (i.e. multi-speed bicycle), all of which attached to the frame. A cyclist, the person who rides the bicycle, provides the input power by turning pedals, thereby cranking the front sprocket (commonly referred to as chainring). The input power provided by the cyclist is equal to the product of angular speed (i.e. the number of pedal revolutions per minute times 2"π") and the torque at the spindle of the bicycle's crankset. The bicycle's drivetrain transmits the input power to the road wheel, which in turn conveys the received power to the road as the output power of the bicycle. Depending on the gear ratio of the bicycle, a (torque, angular speed) pair is converted to a (torque, angular speed) pair. By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles, angular speed of the road wheels is decreased while the torque is increased, product of which (i.e. power) does not change.


title: Torque

text: For SI units, the unit of power is the watt, the unit of torque is the newton metre and the unit of angular speed is the radian per second (not rpm and not revolutions per second).


title: Torque

text: The unit newton-metre is dimensionally equivalent to the joule, which is the unit of energy. In the case of torque, the unit is assigned to a vector, whereas for energy, it is assigned to a scalar. This means that the dimensional equivalence of the newton-metre and the joule may be applied in the former, but not in the latter case. This problem is addressed in , which treats the radian as a base unit rather than as a dimensionless unit.


title: Torque

text: A conversion factor may be necessary when using different units of power or torque. For example, if rotational speed (revolutions per time) is used in place of angular speed (radians per time), we multiply by a factor of 2 radians per revolution. In the following formulas, "P" is power, "τ" is torque, and "ν" (Greek letter nu) is rotational speed.


title: Torque

text: Some people (e.g., American automotive engineers) use horsepower (mechanical) for power, foot-pounds (lbf⋅ft) for torque and rpm for rotational speed. This results in the formula changing to:


title: Torque

text: The constant below (in foot-pounds per minute) changes with the definition of the horsepower; for example, using metric horsepower, it becomes approximately 32,550.


title: Torque

text: The use of other units (e.g., BTU per hour for power) would require a different custom conversion factor.


title: Torque

text: For a rotating object, the "linear distance" covered at the circumference of rotation is the product of the radius with the angle covered. That is: linear distance = radius × angular distance. And by definition, linear distance = linear speed × time = radius × angular speed × time.


title: Torque

text: By the definition of torque: torque = radius × force. We can rearrange this to determine force = torque ÷ radius. These two values can be substituted into the definition of power:


title: Torque

text: The radius "r" and time "t" have dropped out of the equation. However, angular speed must be in radians per unit of time, by the assumed direct relationship between linear speed and angular speed at the beginning of the derivation. If the rotational speed is measured in revolutions per unit of time, the linear speed and distance are increased proportionately by 2 in the above derivation to give:


title: Torque

text: If torque is in newton metres and rotational speed in revolutions per second, the above equation gives power in newton metres per second or watts. If Imperial units are used, and if torque is in pounds-force feet and rotational speed in revolutions per minute, the above equation gives power in foot pounds-force per minute. The horsepower form of the equation is then derived by applying the conversion factor 33,000 ft⋅lbf/min per horsepower:


title: Torque

text: The principle of moments, also known as Varignon's theorem (not to be confused with the geometrical theorem of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques:


title: Torque

text: From this it follows that the torques resulting from two forces acting around a pivot on an object are balanced when


title: Torque

text: Torque can be multiplied via three methods: by locating the fulcrum such that the length of a lever is increased; by using a longer lever; or by the use of a speed reducing gearset or gear box. Such a mechanism multiplies torque, as rotation rate is reduced.


title: Richard Hammond

text: Richard Mark Hammond (born 19 December 1969) is an English journalist, television presenter, mechanic, and writer. He is best known for co-hosting the BBC Two motoring programme "Top Gear" from 2002 until 2015 with Jeremy Clarkson and James May. Since 2016, the trio have presented Amazon Studios' "The Grand Tour".


title: Richard Hammond

text: Hammond has also notably presented entertainment documentary series "" (2003–2008), the game show "Total Wipeout" (2009–2012) and nature documentary series "Planet Earth Live" (2012). In 2016, again with Clarkson and May, Hammond launched the automotive social media website DriveTribe, where he regularly provides content on his tribe "Hammond's Fob Jockeys".


title: Richard Hammond

text: Richard Mark Hammond was born the oldest of three boys on 19 December 1969 in Solihull, England, and is the grandson of workers in the Birmingham car industry. In the mid-1980s Hammond moved with his family (mother Eileen (née Dunsby), father Alan, and younger brothers Andrew, writer of the 'Crypt' series, and Nicholas) to the North Yorkshire cathedral city of Ripon located 10 miles south of the market town of Bedale, and 8 miles south of the historic village of Thornton Watlass where his father ran a probate business in the market square. He attended Blossomfield Infant School in Solihull's Sharmans Cross district from the age of 3–7. Originally a pupil of Solihull School, a fee-paying boys' independent school, he moved to Ripon Grammar School, and from 1986 to 1988 attended Harrogate College of Art and Technology. According to an episode of Top Gear (Season 16, Episode 5), Richard's first job was shoveling grit into a water filtration plant.


title: Richard Hammond

text: After graduation, Hammond worked for several BBC radio stations, including Radio Cleveland, Radio York, Radio Cumbria, Radio Leeds and Radio Newcastle.


title: Richard Hammond

text: Presenting the afternoon programme at Radio Lancashire, his regular guests included motoring journalist Zogg Zieglar, who would review a car of the week by being interviewed by Hammond over the phone. The two became good friends, and it was Zieglar who encouraged Hammond to enter into motoring reviews on television. After starting out on satellite TV, he auditioned for "Top Gear".


title: Richard Hammond

text: Hammond became a presenter on "Top Gear" in 2002, when the show began in its revamped format. He is sometimes referred to as "The Hamster" by fans and his co-presenters on "Top Gear" due to his name and relatively small stature compared to May and Clarkson. His nickname was further reinforced when on three occasions in series 7, he ate cardboard, mimicking hamster-like behaviour.


title: Richard Hammond

text: Following a high-speed dragster crash while filming in September 2006 near York, Hammond returned in the first episode of series 9 (broadcast on 28 January 2007) to a hero's welcome, complete with dancing girls, aeroplane-style stairs and fireworks. The show also contained images of the crash, which had made international headlines, with Hammond talking through the events of the day after which the audience broke into spontaneous applause. Hammond then requested that the crash never be mentioned on the show again, though all three "Top Gear" presenters have since referred to it in jokes during the news segment of the programme. He told his colleagues, "The only difference between me now, and before the crash, is that I like celery now and I didn't before".Following the BBC's decision not to renew Clarkson's contract with the show on 25 March 2015, Hammond's contract expired on 31 March. In April he ruled out the possibility of continuing to present "Top Gear", commenting via Twitter that "amidst all this talk of us 'quitting' or not: there's nothing for me to 'quit' not about to quit my mates anyway". On 12 June 2015 the BBC confirmed that "Top Gear" would return with a 75-minute special, combining two unseen challenges featuring all three presenters from series 22, with studio links from Hammond and May. It aired in the UK on BBC Two on 28 June at 8 p.m, and in the United States on BBC America on 13 July at 9 p.m.


title: Richard Hammond

text: During filming of a "Top Gear" segment at the former RAF Elvington airbase near York on 20 September 2006, Hammond was injured in the crash of the jet-powered car he was piloting. He was travelling at at the time of the crash.


title: Richard Hammond

text: His vehicle, a dragster called "Vampire", was theoretically capable of travelling at speeds of up to . The vehicle was the same car that in 2000, piloted by Colin Fallows, set the British land speed record at . The "Vampire" was powered by a single Bristol-Siddeley Orpheus afterburning turbojet engine producing of thrust.


title: Richard Hammond

text: Some accounts suggested that the accident occurred during an attempt to break the British land speed record, but the Health and Safety Executive report on the crash found that a proposal to try to officially break the record was vetoed in advance by "Top Gear" executive producer Andy Wilman, due to the risks and complexities of such a venture. The report stated: "Runs were to be carried out in only one direction along a pre-set course on the Elvington runway. Vampire’s speed was to be recorded using GPS satellite telemetry. The intention was to record the maximum speed, not to measure an average speed over a measured course, and for (Hammond) to describe how it felt."


title: Richard Hammond

text: Hammond was completing a seventh and final run to collect extra footage for the programme when his front-right tyre failed, and, according to witness and paramedic Dave Ogden, "one of the parachutes had deployed but it went on to the grass and spun over and over before coming to a rest about 100 yards from us." The emergency crew quickly arrived at the car, finding it inverted and partially embedded in the grass. During the roll, Hammond's helmet had embedded itself into the ground, flipping the visor up and forcing soil into his mouth and damaging his left eye. Rescuers felt a pulse and heard the unconscious Hammond breathing before the car was turned upright. Hammond was cut free with hydraulic shears, and placed on a backboard. "He was regaining consciousness at that point and said he had some lower back pain". He was then transported by the Yorkshire Air Ambulance to the neurological unit of the Leeds General Infirmary. Hammond's family visited him at the hospital along with "Top Gear" co-presenters James May and Jeremy Clarkson. Clarkson wished Hammond well, saying "Both James and I are looking forward to getting our 'Hamster' back", referring to Hammond by his nickname. For five weeks while Hammond was recovering in hospital, Clarkson sent a funny message to Mindy, Hammond's wife, every day to try to keep her going. Hammond thought if everyone found out, Clarkson would "die of shame" "cos it makes him look soppy".


title: Richard Hammond

text: The Health & Safety Executive report stated that "Hammond's instantaneous reaction to the tyre blow-out seems to have been that of a competent high performance car driver, namely to brake the car and to try to steer into the skid. Immediately afterwards he also seems to have followed his training and to have pulled back on the main parachute release lever, thus shutting down the jet engine and also closing the jet and afterburner fuel levers. The main parachute did not have time to deploy before the car ran off the runway." The HSE notes that, based on the findings of the North Yorkshire Police (who investigated the crash), "the accident may not have been recoverable", even if Hammond's efforts to react were as fast as "humanly possible".


title: Richard Hammond

text: Hammond made his first TV appearance since the crash on the BBC chat show "Friday Night with Jonathan Ross" on 22 December, just three months after the incident, where he revealed he was in a medically induced coma for two weeks and afterwards suffered from post-traumatic amnesia and a five-second memory. Despite saying he was "absolutely fixed" on the Jonathan Ross episode, in 2011, while talking to the "Daily Mirror", Hammond admitted he had no memory of the interview, saying: "I lost a year. I don’t remember doing the interview with Jonathan Ross or doing Top Gear Live in South Africa" showing the full impact of his brain injury 5 years before.


title: Richard Hammond

text: The crash was shown on an episode of "Top Gear" on 28 January 2007 (Season 9, Episode 1); this was the first episode of the new series, which had been postponed pending Hammond's recovery. Hammond requested at the end of the episode that his fellow presenters never mention the crash again, a request which has been generally observed, although occasional oblique references have been made by all three presenters. "On The Edge: My Story", which contains first-hand accounts from both Hammond and his wife about the crash, immediate aftermath, and his recovery, was published later that year.


title: Richard Hammond

text: In February 2008, Hammond gave an interview to "The Sunday Times" newspaper in which he described the effects of his brain injuries and the progression of his recovery. He reported suffering loss of memory, depression and difficulties with emotional experiences, for which he was consulting a psychiatrist. He also talked about his recovery in a 2010 television programme where he interviewed Sir Stirling Moss and they discussed the brain injuries they had both received as a result of car crashes.


title: Richard Hammond

text: In 2003, Hammond became the first presenter of ""; he was joined by Jon Tickle and Charlotte Hudson in series 2. After the fourth series it was announced that Hammond was no longer going to present the Sky1 show after he signed an exclusive deal with the BBC. Vic Reeves took his place as main presenter.


title: Richard Hammond

text: Early in his career, as well as his radio work, Hammond presented a number of daytime lifestyle shows and motoring programmes such as "Motor Week" on Men & Motors.


title: Richard Hammond

text: He presented the "Crufts" dog show in 2005, the 2004 and 2005 British Parking Awards, and has appeared on "School's Out", a quiz show on BBC One where celebrities answer questions about things they learned at school. He has also presented "". Along with his work on "Top Gear", he presented "Should I Worry About...?" on BBC One, "Time Commanders" on BBC Two and the first four series of "" on Sky 1. He was also a team captain on the BBC Two quiz show, "Petrolheads", in which a memorable part was one where Hammond was tricked into bumping his classic Ferrari while trying to parallel park blindfolded in another car.


title: Richard Hammond

text: In 2006, Hammond fronted the "Richard Hammond's 5 O'Clock Show" with his co-presenter Mel Giedroyc. The programme, which discussed a wide range of topics, was shown every weekday on ITV between 17:00 and 18:00.


title: Richard Hammond

text: He presented "Richard Hammond and the Holy Grail" in 2006. During the special, he travelled to various locations around the world, including the Vatican Secret Archives, exploring the history of the Holy Grail.


title: Richard Hammond

text: As part of Red Nose Day 2007, Hammond stood for nomination via a public telephone vote, along with Andy Hamilton and Kelvin MacKenzie, to be a one-off co-presenter of BBC Radio 4's "Woman's Hour" on 16 March 2007. However, he was defeated by Andy Hamilton.


title: Richard Hammond

text: In April 2007, Hammond presented a one-off special on BBC Radio 2 for Good Friday followed by another in August 2007 for the bank holiday.


title: Richard Hammond

text: Hammond recorded an interview with the famed American stuntman Evel Knievel, which aired on 23 December 2007 on BBC Two, and was Knievel's last interview before his death on 30 November 2007.


title: Richard Hammond

text: In September 2008, Hammond presented the first episode of a new series; "Richard Hammond's Engineering Connections" on the National Geographic Channel. In this show, Hammond discovered how the inventions of the past, along with assistance from nature, help designers today. Episodes include the building of the Airbus A380, Taipei 101 and the Keck Observatory. Series 2 of "Richard Hammond's Engineering Connections" began in May 2010 and has included the building of the Wembley Stadium and the Sydney Opera House.


title: Richard Hammond

text: Hammond appeared in an advertisement for Morrisons supermarkets in 2008, and joined the cast of TV show "Ashes To Ashes" for a special insert on the 2008 Children in Need special.


title: Richard Hammond

text: While in New Zealand for "Top Gear Live 2009", Hammond filmed several television commercials for Telecom New Zealand's new XT UTMS mobile network. Telecom claimed that the new network was "faster in more places", compared to its competitors and its existing CDMA network. After the network suffered three highly publicised outages in late 2009 and early 2010, Hammond became the butt of a joke when he did not return to New Zealand for "Top Gear Live 2010". His fellow "Top Gear" co-hosts said he was too embarrassed to come back to New Zealand, and in a supposed live feed back to Hammond, the feed suddenly drops out as the "XT Network had crashed". Hammond was later given the right of reply to his colleagues during an interview with Marcus Lush on RadioLIVE's breakfast show in New Zealand.


title: Richard Hammond

text: Hammond hosted the UK version of the US series "Wipeout", called "Total Wipeout" for BBC One. It took place in Argentina, and was co-presented by Hammond and Amanda Byram. Hammond presented and performed the voiceover for the clips in a London studio, and Byram was filmed at the obstacle course in Buenos Aires. The series was cancelled at the end of 2012.


title: Richard Hammond

text: Hammond also presented a science-themed game show for children, "Richard Hammond's Blast Lab" which aired on BBC Two and CBBC.


title: Richard Hammond

text: In March 2010, Hammond presented a three-episode series called "Richard Hammond's Invisible Worlds", which looked at things too fast for the naked eye to see, things that are beyond the visible spectrum (e.g., ultraviolet and infra-red light), as well as microscopic things.


title: Richard Hammond

text: One of Hammond's lesser known television roles was as presenter of the BBC Two gameshow "Time Commanders", a sophisticated warfare simulator which used a modified version of Creative Assembly's "" game engine.


title: Richard Hammond

text: Since February 2011, Hammond has presented an online technology series "Richard Hammond's Tech Head". In July 2011, Hammond presented a two-part natural science documentary "Richard Hammond's Journey to the Centre of the Planet", focused on Earth geology and plate tectonics.


title: Richard Hammond

text: In April 2012, Hammond hosted a BBC America programme titled "Richard Hammond's Crash Course", which was also shown in the UK from September 2012 on BBC Two. In May 2012, Hammond co-presented an animal documentary for BBC One called "Planet Earth Live" alongside Julia Bradbury. The programme recorded animals living in extreme conditions.


title: Richard Hammond

text: In June 2014, Hammond presented a scientific fourteen part series on National Geographic Channel titled "Science of Stupid" which focused on the application of physics in everyday life. In December, Hammond presented a three-part science documentary for BBC One called "Wild Weather with Richard Hammond" which focuses on the hidden world of our Earth's extreme weather system.


title: Richard Hammond

text: In September 2015, Hammond presented a two-part documentary for Sky 1 called "Richard Hammond's Jungle Quest", supported by Sky Rainforest Rescue.


title: Richard Hammond

text: In March 2017, whilst filming for "The Grand Tour" in Mozambique, Hammond fell off a motorbike. He reportedly hit his head and was knocked unconscious.


title: Richard Hammond

text: During the season finale of "The Grand Tour" season three, Hammond, James May and Jeremy Clarkson announced the current format was coming to the end and later announced that there would be two more seasons of specials, without the tent or live audience.


title: Richard Hammond

text: In January 2021, Hammond starred alongside "MythBusters" Tory Belleci in "The Great Escapists", a fictional six-episode adventure series for Amazon, which was produced by Chimp Productions. The series stranded the pair on a deserted island where they used the resources they could find to build the means to survive.


title: Richard Hammond

text: On 10 June 2017, Hammond crashed a Rimac Concept One while filming for "The Grand Tour" in Hemberg, Switzerland. Hammond was on his last run up a timed hill climb course during the Bergrennen Hemberg event, when, just after crossing the finish line, the car ran off the road. The car tumbled down the hill and eventually came to rest upside down from the road.


title: Richard Hammond

text: Hammond remained conscious throughout and later described the feeling of "oh god, I'm going to die", as well as being "aware of tumbling – sky, ground, sky, ground, sky, ground, sky, ground." After being airlifted to hospital, Hammond was diagnosed with a tibial plateau fracture in his left knee and a plate and ten screws were surgically inserted.


title: Richard Hammond

text: Jeremy Clarkson and James May, fellow presenters on "The Grand Tour" both witnessed the scene from afar, and, believing Hammond was dead, May recalled feeling a "blossoming, white-hot ball of pure, sickening horror forming in my heart" with Clarkson describing his "knees turning to jelly" at the sight of the crash.


title: Richard Hammond

text: After the ordeal, the FIA allegedly ruled that the "show runs" Hammond and company were doing at the time of the accident violated the governing body's International Sporting Code and that the crash "acted against the interests of the sport." As a result, the Bergrennen Hemberg organizers were fined $5,138, on top of six-month license suspensions for race director Christian Müller and stewards Hermann Müller, Karl Marty, and Daniel Lenglet. In August of that year, Motorsport.com reported that the future of the entire event "is now in jeopardy." Despite the reports, the Bergrennen Hemberg would be held again in 2018, and driver registrations opening for 2019.


title: Richard Hammond

text: Hammond announced on Twitter on 21 June 2021 that he would be making a show with Discovery+ about the restoration of old cars.


title: Richard Hammond

text: Hammond has been married to Amanda "Mindy" Hammond (born Etheridge, born 6 July 1965), a columnist for the "Daily Express", since May 2002. They have two daughters, Isabella "Izzy" (born 2001) and Willow (born 2004).


title: Richard Hammond

text: It was his friend Zogg Zieglar who first gave Hammond his nickname Hamster. After the couple announced the impending birth of their first child, Zieglar's response was "And out will pop another hamster." The nickname stuck, especially on "Top Gear" due to his name and relatively small stature compared to May and Clarkson. His nickname was further reinforced when on three occasions in series 7, he ate cardboard, mimicking hamster-like behaviour.


title: Richard Hammond

text: Hammond is known for owning a large number of animals on Bollitree Farm including several horses, dogs, cats, chickens, ducks, sheep, and a peacock. He and his family adopted TG, the official "Top Gear" dog, after it became apparent that the labradoodle was afraid of cars. The dog died at age 11 in January 2017.


title: Richard Hammond

text: Hammond plays bass guitar, on which he accompanied the other "Top Gear" presenters when they performed alongside Justin Hawkins on "Top Gear of the Pops" for Comic Relief in 2007.


title: Richard Hammond

text: He likes to ride his bicycle, scooter, or motorbike in cities, for which he is mocked mercilessly by fellow presenter Jeremy Clarkson.


title: Richard Hammond

text: During the news segment of special, Hammond openly expressed his dislike of the band Genesis. This fact was later exploited by his co-presenters (particularly by Clarkson) in three special episodes: during the , when they installed a secret second stereo unit in his Fiat Barchetta that only plays the band's "Live over Europe 2007" album; in the , Clarkson played the same song used in the previous special (albeit the "Seconds Out" version) through the megaphone mounted in his Jaguar XJS, despite Hammond driving a different car (a Mini Cooper Sport). In the 2013 Africa Special, Clarkson once again played Genesis in an attempt to get Hammond to let him pass.


title: Richard Hammond

text: In 2007, Hammond went to Africa on a , with his choice of car being a 1963 Opel Kadett, which he subsequently named Oliver. A week after the special was aired, Hammond announced during the news section that he had shipped Oliver back to the UK, where it was restored by a team from "Practical Classics" magazine. Oliver features on Hammond's children's science television show "Richard Hammond's Blast Lab" and in another episode of "Top Gear" as a kind of "Hill-holder" in the trailer truck challenge (after it acquired the fake personal plate "OLI V3R"). Oliver is also mentioned in Hammond's second autobiography "As You Do".


title: Richard Hammond

text: In 2010, Hammond was the president of the 31st Herefordshire Country Fair held at Hampton Court in Hope under Dinmore. His involvement caused unprecedented attendance with "nearly 15,000 people" drawn to the event to meet the presenter.


title: Richard Hammond

text: In March 2012, Hammond passed his B206 LST helicopter licence and has since owned a Robinson R44 Raven II helicopter.


title: Richard Hammond

text: In September 2018, his wife reported that she and Richard, along with their fifteen-year-old daughter, had been burgled while sleeping at a holiday villa in Saint-Tropez, speculating that they might have been rendered unconscious by noxious gas.


title: Richard Hammond

text: The Hammond family lives in a mock castle in Herefordshire and they also have an apartment in London. In an interview with "The Sunday Times" in February 2008, it was reported that Hammond had moved briefly from Gloucestershire to Buckinghamshire, then back again, because he missed the country life.


title: Richard Hammond

text: In October 2012, it was reported he had spent over £2 million buying Bollitree Castle which is situated near Weston under Penyard, Ross-on-Wye. It has been rumoured he has also bought a large house in the small town of Wantage, Oxfordshire.


title: Richard Hammond

text: Hammond is an ambassador of UK charity for children with brain injury and neuro-disability The Children's Trust.


title: Richard Hammond

text: On 29 September 2013, terminally-ill eight-year-old Emilia Palmer was driven by Hammond in a pink Lamborghini Aventador Roadster (newly repainted for the occasion). Hammond flew his Robinson R44 helicopter, G-OHAM, to Shobdon Aerodrome, then picked Palmer up from her home in Kimbolton, Herefordshire and drove her back to the airport for a high-speed run on the main runway. The event was arranged at short notice by Rays of Sunshine.


title: Richard Hammond

text: Hammond's comments and actions have sometimes resulted in complaints from viewers, LGBT rights charities, and foreign diplomats.